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.

A spherical cavity expansion model for penetration of ogival-nosed projectiles into concrete targets with shear-dilatancy

A dynamic spherical cavity-expansion penetration model is suggested herein to predict the penetration and perforation of concrete targets struck normally by ogivalnosed projectiles.Shear dilatancy as well as compressibility of the material in comminuted region are considered in the paper by introducing a dilatant-kinematic relation.A procedure is first presented to compute the radial stress at the cavity surface and then a numerical method is used to calculate the results of penetration and perforation with friction being taken into account.The influences of various target parameters such as shear strength,bulk modulus,density,Poisson＇s ratio and tensile strength on the depth of penetration are delineated.It is shown that the model predictions are in good agreement with available experimental data.It is also shown that the shear strength plays a dominant role in the target resistance to penetration.

Analytical solutions for finite cylindrical dynamic cavity expansion in compressible elastic-plastic materials

Analytical solutions for the dynamic cylindrical cavity expansion in a com-pressible elastic-plastic cylinder with a finite radius are developed by taking into account of the effect of lateral free boundary, which are different from the traditional cavity expan-sion models for targets with infinite dimensions. The finite cylindrical cavity expansion process begins with an elastic-plastic stage followed by a plastic stage. The elastic-plastic stage ends and the plastic stage starts when the plastic wave front reaches the lateral free boundary. Approximate solutions of radial stress on cavity wall are derived by using the Von-Mise yield criterion and Forrestal’s similarity transformation method. The effects of the lateral free boundary and finite radius on the radial stress on the cavity wall are discussed, and comparisons are also conducted with the finite cylindrical cavity expansion in incompressible elastic-plastic materials. Numerical results show that the lateral free boundary has significant influence on the cavity expansion process and the radial stress on the cavity wall of metal cylinder with a finite radius.

Influence of particle contact models on soil response of poorly graded sand during cavity expansion in discrete element simulation

The discrete element method(DEM) has been extensively adopted to investigate many complex geotechnical related problems due to its capability to incorporate the discontinuous nature of granular materials. In particular, when simulating large deformations or distortion of soil(e.g. cavity expansion),DEM can be very effective as other numerical solutions may experience convergence problems. Cavity expansion theory has widespread applications in geotechnical engineering, particularly to the problems concerning in situ testing, pile installation and so forth. In addition, the behaviour of geomaterials in a macro-level is utterly determined by microscopic properties, highlighting the importance of contact models. Despite the fact that there are numerous contact models proposed to mimic the realistic behaviour of granular materials, there are lack of studies on the effects of these contact models on the soil response.Hence, in this study, a series of three-dimensional numerical simulations with different contact constitutive models was conducted to simulate the response of sandy soils during cylindrical cavity expansion. In this numerical investigation, three contact models, i.e. linear contact model, rolling resistance contact model,and Hertz contact model, are considered. It should be noted that the former two models are linear based models, providing linearly elastic and frictional plasticity behaviours, whereas the latter one consists of nonlinear formulation based on an approximation of the theory of Mindlin and Deresiewicz. To examine the effects of these contact models, several cylindrical cavities were created and expanded gradually from an initial radius of 0.055 m to a final radius of 0.1 m. The numerical predictions confirm that the calibrated contact models produced similar results regarding the variations of cavity pressure, radial stress, deviatoric stress, volumetric strain, as well as the soil radial displacement. However, the linear contact model may result in inaccurate predictions when highly angular soil particles are involved. In addition, considering the excessive soil displacement induced by the pile installation(i.e. cavity expansion), a minimum distance of11 a(a is the cavity radius) is recommend for practicing engineers to avoid the potential damages to the existing piles and adjacent structures.

Research on the Generation Mechanism and Suppression Method of Aerodynamic Noise in Expansion Cavity Based on Hybrid Method

The expansion chamber serves as the primary silencing structure within the exhaust pipeline.However,it can also act as a sound-emitting structure when subjected to airflow.This article presents a hybrid method for numerically simulating and analyzing the unsteady flow and aerodynamic noise in an expansion chamber under the influence of airflow.A fluid simulation model is established,utilizing the Large Eddy Simulation(LES)method to calculate the unsteady flow within the expansion chamber.The simulation results effectively capture the development and changes of the unsteady flow and vorticity inside the cavity,exhibiting a high level of consistency with experimental observations.To calculate the aerodynamic noise sources within the cavity,the flow field results are integrated using the method of integral interpolation and inserted into the acoustic grid.The acoustic analogy method is then employed to determine the aerodynamic noise sources.An acoustic simulation model is established,and the flow noise source is imported into the sound field grid to calculate the sound pressure at the far-field response point.The calculated sound pressure levels and resonance frequencies show good agreement with the experimental results.To address the issue of airflow regeneration noise within the cavity,perforated tubes are selected as a means of noise suppression.An experimental platformfor airflow regeneration noise is constructed,and experimental samples are processed to analyze and verify the noise suppression effect of perforated tube expansion cavities under different airflow velocities.The research findings indicate that the perforated tube expansion cavity can effectively suppress low-frequency aerodynamic noise within the cavity by impeding the formation of strong shear layers.Moreover,the semi-perforated tube expansion cavity demonstrates the most effective suppression of aerodynamic noise.

Semi-analytical solution for drained expansion analysis of a hollow cylinder of critical state soils

The expansion of a thick-walled hollow cylinder in soil is of non-self-similar nature that the stress/deformation paths are not the same for different soil material points.As a result,this problem cannot be solved by the common self-similar-based similarity techniques.This paper proposes a novel,exact solution for rigorous drained expansion analysis of a hollow cylinder of critical state soils.Considering stress-dependent elastic moduli of soils,new analytical stress and displacement solutions for the nonself-similar problem are developed taking the small strain assumption in the elastic zone.In the plastic zone,the cavity expansion response is formulated into a set of first-order partial differential equations(PDEs)with the combination use of Eulerian and Lagrangian descriptions,and a novel solution algorithm is developed to efficiently solve this complex boundary value problem.The solution is presented in a general form and thus can be useful for a wide range of soils.With the new solution,the non-self-similar nature induced by the finite outer boundary is clearly demonstrated and highlighted,which is found to be greatly different to the behaviour of cavity expansion in infinite soil mass.The present solution may serve as a benchmark for verifying the performance of advanced numerical techniques with critical state soil models and be used to capture the finite boundary effect for pressuremeter tests in small-sized calibration chambers.

PREDICTION OF PROJECTILE PENETRATION AND PERFORATION BY FINITE CAVITY EXPANSION METHOD WITH THE FREE-SURFACE EFFECT

With a target treated as the incompressible Tresca and Mohr-Coulomb material, by assuming that cavity expansion produces plastic-elastic and plastic-cracked-elastic response region, the decay function for the free-surface effect is constructed for metal and geological tar- gets, respectively. The forcing function for oblique penetration and perforation is obtained by multiplying the forcing function derived on the basis of infinite target assumption with the de- cay function. Then the projectile is modeled with an explicit transient dynamic finite element code and the target is represented by the forcing function as the pressure boundary condition. This methodology eliminates discretizing the target as well as the need for a complex contact algorithm and is implemented in ABAQUS explicit solver via the user subroutine VDLOAD. It is found that the free-surface effect must be considered in terms of the projectile deformation, residual velocity, projectile trajectory, ricochet limits and critical reverse velocity. The numerical predictions are in good agreement with the available experimental data if the free-surface effect is taken into account.

An undrained expansion solution of cylindrical cavity in SANICLAY for K_(0)-consolidated clays

This paper proposes a rigorous undrained solution for cylindrical cavity expansion problems in K_(0)-consolidated clays,adopting a simple non-associated and anisotropic model,SANICLAY.The cavity expansion theory is well extended to consider non-associativity,K_(0)-consolidation and stress-induced anisotropy with combined rotational and distortional hardening of yield surface and plastic potential in the multiaxial stress space.The developed solution can be recovered for validation against the modified Cam-clay(MCC)solution by simply setting model constants,avoiding non-associativity and anisotropy.The source code is provided to facilitate the use for extensions.After investigating the effects of overconsolidation ratio on the cavity pressure curves,stress distributions,evolutions of anisotropic parameters and stress paths,the variations with three-dimensional(3D)evolutions of yield surface and plastic potential during undrained cavity expansion are shown for various K_(0)-consolidated clays.A parametric study on the model constants is presented to depict the influences on the stress distributions and paths,critical state surfaces and Lode’s angles at failure.The proposed solution also provides a general framework for formulating equations for undrained expansion of cylindrical cavities under an initial cross anisotropic condition using sophisticated anisotropic soil models.It serves as a precise benchmark for extensions of analytical solutions,numerical simulations of cavity expansion,and backcalculations of geotechnical problems.

Finite Spherical Cavity Expansion Method for Layering Effect

A decay function for the layering effect during the projectile penetrating into layered targets is constructed, which is obtained via the theoretical solution of a dynamically expanding layered spherical cavity with finite radius in the layered targets that are assumed to be incom- pressible Mohr-Coulomb materials. By multiplying the decay function with the semi-empirical forcing functions that account for all the constitutive behavior of the targets, the forcing functions for the layered targets are obtained. Then, the forcing functions are used to represent the targets and are applied on the projectile surface as the pressure boundary condition where the projectile is modeled by an explicit transient dynamic finite element code. This methodology is implemented into ABAQUS explicit solver via the user subroutine VDLOAD, which eliminates the need for discretizing the targets and the need for the complex contact algorithm. In order to verify the proposed layering effect model, depth-of-penetration experiments of the 37 mm hard core pro-jectile penetrating into three sets of fiber concrete and soil layered targets are conducted. The predicted depths of penetration show good agreement with the experimental data. Furthermore, the influence of layering effect on projectile trajectory during earth penetration is investigated. It is found that the layering effect should be taken into account if the final position and trajectory of the projectile are the main concern.

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.

Model for Long-Rod Penetration into Semi-Infinite Targets

Based on the equation of momentum conservation, an improved equation for the quisi-steady penetration of a long rod into homogeneous semi-infinite targets has been derived, assuming that the flow interface between the rod material and the target material is hemispherical and that the normal pressure on the interface is defined by the dynamic spherical cavity expansion. The equation has a form similar to the Tate equation, and the parameters in this equation have definite physical senses and practical values..

Resistance of grid steel-tube-confined concrete targets against projectile impact: Experimental investigation and analytical engineering model

Steel-tube-confined concrete(STCC) targets are provided with excellent anti-penetration performance over semi-infinite concrete(SIC) targets since the steel tube imposes passive restraint on the in-filled concrete during the penetration process. Grid STCC system with square steel tubes is a potential solution to protective structures. In this paper, experiments of 9-cell grid STCC targets penetrated by 12.7 mm Armor Piercing Projectile(APP) were performed. The influence of side length and thickness of steel tube,steel ratio and impact velocity on anti-penetration performance were taken into account. Additionally,single-cell square STCC targets were also designed and tested for comparison with the 9-cell grid STCC targets. Damage modes and parameters of the tested targets were measured and discussed. Moreover,the stiffness of radial confinement of grid STCC targets is achieved according to the elastic solution of infinite cylindrical shell in Winkler medium. Furthermore, the penetration resistance and depth of penetration(DOP) for grid STCC targets are obtained on the basis of the dynamic finite spherical cavityexpansion(FSCE) models including radial confinement effect. It is shown that the 9-cell grid STCC targets with optimal dimension match of thickness and side length of steel tube can reduce the DOP by about17 % and 23 % in comparison with the SIC targets and single-cell square STCC targets, respectively, due to both the confinement of square steel tube to concrete in the impacted cell and the additional confinement of the surrounding cells to the impacted cell;the penetration resistance and DOP of the grid and cellular STCC targets with similar steel ratio is close, and thus the grid STCC targets with simpler manufacturing process and excellent in-plane expandability are preferred in engineering practice;moreover, the predicted results of DOP model based on the FSCE models agree well with the tested results with the maximum disparity less than 12 % and the proposed model is more applicable to the grid and cellular STCC targets with high radial confinement.

Poroelastic solution of a wellbore in a swelling rock with non-hydrostatic stress field

The stress distribution around a circular borehole has been studied extensively. The existing analytical poroelastic solutions, however, often neglect the complex interactions between the solid and fluid that can significantly affect the stress solution. This is important in unconventional gas reservoirs such as coalbeds and shale formations. In order to address this limitation, this paper presents the development of a poroelastic solution that takes into account the effect of gas sorption-induced strain. The solution considers drainage of the reservoir fluid through a vertical wellbore in an isotropic, homogenous,poroelastic rock with non-hydrostatic in situ stress field. The sorption-induced shrinkage of coal is modelled using a Langmuir-type curve which relates the volumetric change to the gas pressure. The redistributed stress field around the wellbore after depletion is found by applying Biot’s definition of effective stress and Airey’s stress functions, which leads to a solution of the inhomogeneous Biharmonic equation. Two sets of boundary conditions were considered in order to simulate the unsupported cavity(open-hole) and supported cavity(lined-hole) cases. The implementation was verified against a numerical solution for both open-hole and lined-hole cases. A comparative study was then conducted to show the significance of the sorption-induced shrinkage in the stress distribution. Finally, a parametric study analysed the sensitivity of the solution to different poroelastic parameters. The results demonstrate that the developed solution is a useful tool that can be employed alongside complex flow models in order to conduct efficient, field-scale coupled hydro-mechanical simulations, especially when the stressdependent permeability of the reservoir is of concern.

Optimization of inter-helix spacing for helical piles in sand

The optimization of the inter-helix spacing is a key issue of the axial bearing capacity of helical piles.In this paper,based on the cavity expansion,an analytical approach considering the small-strain stiffness,strength,compressibility and stress level of sand around the helical pile was proposed to analyze the influence zone of the helices to determine the optimal inter-helix spacing in sand.The calculation results of the proposed method were verified using the centrifuge test data and finite element analysis for helical pile in Congleton HST95 sand.They were also compared with those using the Meyerhof pile foundation theory.The results show that the optimal inter-helix spacing based on Meyerhof pile foundation theory differs significantly from the measurement.The range of the influence zone for the helices in sand calculated by the cavity expansion theory matches with the data from literature.The calculation results with the proposed method are consistent with the range of the optimal spacing ratio inferred in the centrifuge tests.The results based on the two-dimensional(2D)finite element model(FEM)are also basically consistent with the calculated analytical solution.

Grouted Pile and Its Bearing Capacity

The grouting method applied in bored pile is an improvement to the conventional bored pile. Load tests have proved that grouting under the bored pile tip is an effective method to enhance the bearing capacity of the pile and to reduce the pile settlement. In this paper, the grouting technology is described and pile load test results are discussed. In order to put the grouting method into design practice, the authors analyze the working mechanism of soil compaction. And, based on the theory of cavities expansion in soil mass, approximate formulae are proposed for estimating the bearing capacity of the grouted pile. The theoretical prediction agrees well with the load test results.

Assessing the range of blasting-induced cracks in the surrounding rock of deeply buried tunnels based on the unified strength theory

Blasting-induced cracks in the rock surrounding deeply buried tunnels can result in water gushing and rock mass collapse,posing significant safety risks.However,previous theoretical studies on the range of blasting-induced cracks often ignore the impact of the in-situ stress,especially that of the intermediate principal stress.The particle displacement−crack radius relationship was established in this paper by utilizing the blasthole cavity expansion equation,and theoretical analytical formulas of the stress−displacement relationship and the crack radius were derived with unified strength theory to accurately assess the range of cracks in deep surrounding rock under a blasting load.Parameter analysis showed that the crushing zone size was positively correlated with in-situ stress,intermediate principal stress,and detonation pressure,whereas negatively correlated with Poisson ratio and decoupling coefficient.The dilatancy angle-crushing zone size relationship exhibited nonmonotonic behavior.The relationships in the crushing zone and the fracture zone exhibited opposite trends under the influence of only in-situ stress or intermediate principal stress.As the in-situ stress increased from 0 to 70 MPa,the rate of change in the crack range and the attenuation rate of the peak vibration velocity gradually slowed.

Microcellular injection molding process for producing lightweight thermoplastic polyurethane with customizable properties

A three-stage molding process involving microcellular injection molding with core retraction and an ＂out-of-mold＂ expansion was developed to manufacture thermoplastic polyurethane into lightweight foams of varying local densities, microstructures, and mechanical properties in the same microcellular injection molded part. Two stages of cavity expansion through sequential core retractions and a third expansion in a separate mold at an elevated temperature were carried out. The densities varied from 0.25 to 0.42 g/cm3 （77% to 62% weight reduction）. The mechanical properties varied as well Cyclic com- pressive strengths and hysteresis loss ratios, together with the microstructures, were characterized and reported.

Hydraulic fracturing pressure of concentric double-layered cylinder in cohesive soil

This study aims to investigate hydrofracturing in double-layered soil through theoretical and experimental analysis,as multilayered soils where the difference in mechanical properties exists are generally encountered in practical engineering.First,an analytical solution for fracturing pressure in two different concentric regions of soil was presented based on the cavity expansion theory.Then,several triaxial hydraulic fracturing tests were carried out to validate the analytical solution.The comparison between the experimental and analytical results indicates the remarkable accuracy of the derived formula,and the following conclusions were also obtained.First,there is a linear relationship between the fracturing pressure and confining pressure in concentric double-layered cohesive soil.Second,when the internal-layer soil is softer than the external-layer soil,the presence of internal soil on the fracturing pressure approximately brings the weakening effect,and the greater strength distinction between the two layers,the greater the weakening effect.Third,when the internal-layer soil is harder than the external-layer soil,the existence of the internal-layer soil has a strengthening effect on the fracturing pressure regardless of the proportion of internal-layer soil.Moreover,the influence of strength distinction between the two layers on the fracturing pressure is significant when the proportion of internal-layer soil is less than half,while it’s limited when the proportion is more than half.The proposed solution is potentially useful for geotechnical problems involving aspects of cohesive soil layering in a composite formation.

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.

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.