Spherical Expansion Research Articles

Spudcan-pile interaction in thick soft clay and soft clay overlying sand: A simplified numerical solution

A drilling jack-up is often deployed to perform drilling activities or well intervention at an existing fixed jacket platform. Depending on the clearance distance between the aft spudcan and the nearest pile, the installation of the spudcan may have an adverse effect on the platform pile which in turn could compromise the integrity of the jacket structure. This paper presents a simplified method for assessing the effect of spudcan installation on the pile foundation of a jacket platform in thick soft clay and soft clay overlying sand layers. Adopting a two-stage uncoupled approach, in which predetermined free-field lateral soil displacements are applied to a beam-column model with soil modelled using p-y curves, the soil displacements around a penetrating spudcan is estimated by an analytical solution derived from spherical cavity expansion theory. With appropriate consideration for the volume of soil displaced by the penetrating spudcan for the cases of thick soft clay and consideration for soil squeezing for soft clay overlying sand, the computed free-field lateral soil displacements are in fair agreement with the measured profiles in centrifuge tests and can be used in a beam-column model to estimate the induced bending moment in the pile in practice.The pile response to the free-field lateral soil displacements is assessed using a beam-column model incorporating p–y curves, considering the effect of soil remoulding caused by the installation of the spudcan where appropriate. A numerical model which considers the evolving lateral soil displacements due to the progressive advancement of the penetrating spudcan is also studied. The computed pile bending moment profiles are consistent with the measured profiles in the centrifuge tests and those computed by 3D large deformation finite element (LDFE) model. The proposed practical method is simple but yet effective to assess the influence of the installation of a spudcan foundation on an adjacent pile of a jacket platform in thick soft clay and soft clay overlying sand.

Study of the Bearing Capacity at the Variable Cross-Section of A Riser-Surface Casing Composite Pile

Reducing the cost of offshore platform construction is an urgent issue for marginal oilfield development. The offshore oil well structure includes a riser and a surface casing. The riser, surface casing and oil well cement can be considered special variable cross-section piles. Replacing or partially replacing the steel pipe pile foundation with a variable cross-section pile to provide the required bearing capacity for an offshore oil platform can reduce the cost of foundation construction and improve the economic efficiency of production. In this paper, the finite element analysis method is used to investigate the variable cross-section bearing mode of composite piles composed of a riser and a surface casing in saturated clay under a vertical load. The calculation formula of the bearing capacity at the variable section is derived based on the theory of spherical cavity expansion, the influencing factors of the bearing capacity coefficient Nc are revealed, and the calculation method of Nc is proposed. By comparing the calculation results with the results of the centrifuge test, the accuracy and applicability of the calculation method are verified. The results show that the riser composite pile has a rigid core in the soil under the variable cross-section, which increases the bearing capacity at the variable cross-section.

Undrained Spherical Cavity Expansion in Unsaturated Soils: Semianalytical Solution Coupling Hydraulic and Mechanical Behaviors

A coupled hydromechanical solution to undrained spherical cavity expansion problem in unsaturated soil is proposed with an elastoplastic model for unsaturated soil. The mechanical response and hydraulic behavior of soil during expansion are coupled together through a soil–water characteristic curve (SWCC) that evolves with the void ratio. A system of four first-order differential governing equations is derived based on the equilibrium equation, large stain theory and coupled hydromechanical constitutive relationship of soil. The present solution can reduce to unified hardening parameter model based solution under saturated condition, which validates the proposed solution. The effects of overconsolidation ratio and initial suction on expansion responses are explored based on extensive parametric studies. Special attention is paid to investigate the distributions of the principal stresses, suction, and saturated degree of soil around the expanded cavity; the stress trajectory of a representative element at the cavity surface; and cavity pressure–displacement curves. The proposed analytical solution can serve as a theoretical framework for modelling of some fundamental geotechnical problems in unsaturated soils using critical state soil models.

Numerical study on undrained cone penetration in structured soil using G-PFEM

This paper presents a model for the numerical simulation of cone penetration in structured soil under undrained conditions based on the Particle Finite Element Method. An extended version of the Clay and Sand Model (CASM), allowing microstructural bonding and its degradation to be taken into account, was implemented into the application G-PFEM and compared to the analytical solution for undrained spherical cavity expansion. A robust model for cone penetration is obtained using a nonlocal stress-integration combined with the IMPLEX integration scheme. A parametric study on the shape of the yield surface – which is adaptable for the CASM – and the degree of initial bonding, as well as the rate of destructuration, was conducted to investigate the influence on the obtained normalized parameters Qt, BQ, U, and the cone factors Nkt, NΔu, Nke used for the determination of the undrained shear strength. It was found that the highest cone factors, leading to conservative estimations of the peak undrained shear strength, are obtained for unbonded material. Both, the shear strength and the tip resistance increase due to soil structure, however, Nkt and Nke are not significantly influenced as long as no destructuration takes place during penetration.

Acoustic radiation torque on a compressible spheroid.

Starting with the theoretical framework for calculating the acoustic radiation force on a compressible spheroid [Jerome et al., J. Acoust. Soc. Am. 148, 2403-2415 (2020)], the present work develops a model for the corresponding acoustic radiation torque. A general result is obtained that may be applied to an object of arbitrary size, shape, and impedance in an arbitrary incident sound field. Like for the radiation force, the general result for the radiation torque is a summation of terms involving products of the coefficients in spherical wave expansions of the incident and scattered fields. For the compressible spheroid under consideration, spheroidal wave expansions are employed to satisfy the boundary conditions on the surface of the spheroid to obtain the scattering coefficients. Results are presented for the radiation torque exerted on a compressible spheroid by a progressive or standing incident plane wave. The results illustrate the dependence of the radiation torque on the size, aspect ratio, and impedance of the spheroid and on its orientation with respect to the incident wave field.

Cavitation phenomenon in penetration of rigid projectiles into elastic-plastic targets

This paper presents an analytical study on the cavitation phenomenon during penetration of a rigid projectile into an elastic-plastic target. The developed analytical approach is based on the general solution of the quasi-static and non-stationary dynamic cylindrical/spherical cavity expansion problem with assigned kinematic boundary condition at the cavity boundary (variable, time dependent radial velocity). An analytical projectile-target separation criterion is developed for a projectile having an arbitrary shape and for a target described by a simplified material model with a locked equation of state and a linear shear failure relationship. This relatively simple model may represent the behavior of different materials reasonably well yet allow an analytical solution of the problem. The paper derives the analytical expression of the contact zone size using both the cylindrical and spherical cavity expansion approaches and presents the related normal contact stresses acting on the projectile nose surface that maintains contact with the target. Examples of the developed formulation is presented for ogive nose and Rankine ovoid projectiles hitting aluminum targets, with a constant shear failure envelope, at different velocities and comparisons with known analytical and numerical solutions are shown. The effect of projectile and medium properties on the size of the contact zone are studied.

Cellularization characteristics of ethyl acetate spherical expanding flame

The cellular instability of ethyl acetate (EA) premixed flame has been studied theoretically and experimentally under different initial temperature, pressure and equivalence ratio. The constant pressure method (CPM) was used to determine the laminar burning velocity of EA spherical expanding flame in this research. In addition, the cellular evolution image of EA spherical expansion flame surface was obtained using high-speed schlieren technology. The image processing technology combined with three-dimensional reconstruction algorithm was used to extract and reconstruct the flame surface crack length, the number of cells on the flame surface, cellular area and cellular length scale. From the quantitative analysis of surface crack and cellular structure of EA flame, it can be seen that the evolution of flame surface crack and surface cellular structure is largely affected by equivalence ratio and initial pressure. With the increase of initial pressure or equivalence ratio, the earlier the flame surface cracks and cell formation. Furthermore, according to the cellular length scale in different radius, the wavenumber was deduced, and compared with the theoretical curve, it is found that the experimental wave numbers have the same evolution trend. Although, when the equivalence ratio is 1.4 with high Peclet number, the experimental wave numbers are somewhat beyond the boundary of the peninsula curve due to the influence of the nonlinear effects, the trend is consistent with the theoretical results.

Calculation method for the vertical bearing capacity of a riser-surface casing composite pile

ABSTRACT The variable cross-section structure (comprising a riser, surface casing and cementing cement ring) of an oil well associated with an offshore oil platform is similar to that of a steel pipe pile foundation. If a well structure with variable cross-section characteristics can be used to provide bearing capacity, the construction cost of platforms will be reduced. In this paper, the finite element analysis method is used to study the vertical bearing mechanism of composite piles composed of a riser and a surface casing in saturated clay and sand. Based on the theory of spherical cavity expansion, the calculation methods of end resistance and skin friction resistance of composite pile are established. Finally, based on a field test of the bearing capacity of composite piles, the accuracy of the proposed calculation method is verified.

A semi-analytical solution to spherical cavity expansion in unsaturated soils

This paper presents a rigorous solution for spherical cavity expansion in unsaturated soils under constant suction condition. The hydraulic behavior that describes the saturation-suction relationship is modeled by a void ratio-dependent soil-water characteristic curve, which allows the hydraulic behavior to fully couple with the mechanical behavior that is described by an extended critical state soil model for unsaturated soil through the specific volume. Considering the boundary condition and introducing an auxiliary coordinate, the problem is formulated to a system of first-order differential equations with three principal stress components and suction as basic unknowns, which is solved as an initial value problem. Parameter analyses are conducted to investigate the effects of suction and the overconsolidation ratio on the overall expansion responses, including the pressure-expansion response, the distribution of the stress components around the cavity, and the stress path of the soil during cavity expansion. The results reveal that the expansion pressures and the distribution of the stress components in unsaturated soils are generally higher than those in saturated soils due to the existence of suction.

A similarity solution for spherical cavity drained expansion in overconsolidated soils considering large deformation

This paper presents a novel similarity solution for drained spherical cavity expansion in overconsolidated soils, which creatively incorporates the large strain into similarity solution. The salient feature of the present solution lies in that it properly represents the large deformation associated responses of the overconsolidated soil during cavity expansion. The logarithmic strain components are reasonably incorporated into the similarity solution, which is a general solution technique that has been widely used to solve cavity expansion problems, to creatively account for the large deformation of soils during cavity expansion in such a solution framework. The competent modified unified-hardening (UH) model is employed to properly represent the unique behavior of overconsolidated soils during expansion, where three-dimensional strength characteristics of the soil are taken into account as well. The partial differential governing equations under Eulerian description are transformed into a set of first order ordinary differential equations under Lagrangian description and further solved as an initial value problem by MATLAB. The present method is verified by comparing with the modified Cam-clay model based solutions and an extensive parameter analysis is subsequently conducted for soils with different overconsolidation ratio. The unique expansion behaviors in the overconsolidated soils including the peak strength behavior, strain-hardening/softening and shear dilatancy behaviors are discussed in a comprehensive and in-depth manner.

Assessment of mmWave Exposure From Antenna Based on Transformation of Spherical Wave Expansion to Plane Wave Expansion

To protect human beings from overexposure to mmWave electromagnetic fields, international guidelines and standard specified the (exposure) reference level in terms of the peak spatial-average incident power density ( ps PD). In this study, we proposed a method to effectively assess the ps PD from a mmWave antenna using its spherical near-field measurement data. This method employed the transformation of spherical wave expansion to plane wave expansion to reconstruct the electric and magnetic field components on an evaluation plane in front of the antenna aperture. The ps PD was subsequently obtained based on the time-average Poynting vector. The accuracy of the proposed method was validated by comparing it with full-wave simulation results using 12 array antennas at frequencies ranging from 10 to 90 GHz. It was revealed that at 30 GHz, the reconstruction errors for ps PD4cm2 were less than 0.8 dB and 0.2 dB on evaluation planes 2 and 5 mm, respectively, in front of the antennas. The robustness of the proposed method against the noise, scan range, and number of spherical modes were evaluated. The proposal may eliminate conventional compliance assessment procedures once antenna performance is evaluated in spherical near-field measurement.

Near-Field to Far-Field RCS Prediction on Arbitrary Scanning Surfaces Based on Spherical Wave Expansion.

Near-field to far-field transformation (NFFFT) is a frequently-used method in antenna and radar cross section (RCS) measurements for various applications. For weapon systems, most measurements are captured in the near-field area in an anechoic chamber, considering the security requirements for the design process and high spatial costs of far-field measurements. As the theoretical RCS value is the power ratio of the scattered wave to the incident wave in the far-field region, a scattered wave measured in the near-field region needs to be converted into field values in the far-field region. Therefore, this paper proposes a near-field to far-field transformation algorithm based on spherical wave expansion for application in near-field RCS measurement systems. If the distance and angular coordinates of each measurement point are known, the spherical wave functions in an orthogonal relationship can be calculated. If each weight is assumed to be unknown, a system of linear equations as numerous as the number of samples measured in the near electric field can be generated. In this system of linear equations, each weight value can be calculated using the iterative least squares QR-factorization method. Based on this theory, the validity of the proposed NFFFT is verified for several scatterer types, frequencies and measurement distances.

Fast Characterization of Mutually Coupled Array Antennas Using Isolated Antenna Far-Field Data

A new method is proposed to analyze antenna arrays including mutual coupling (MC), which is based on the concept of multiple scattering, and relates to the iterative Jacobi and Gauss-Seidel methods. The method employs sampled far-field data of an isolated element, which can be obtained by any full-wave simulator and consists of far fields for excitation at the antenna feed and for plane waves with different angles of incidence. Mutual interactions between the array elements are modeled by approximating the incident field as a single dual-polarized plane wave taken from the spherical wave expansion of the scattered field from any other element in the array. The accuracy and run-time performances of the method are evaluated mainly by comparing simulations for several array geometries to method of moments (MoM)-based full-wave solutions. The method is primarily intended as a tool for the fast sequential analysis of arrays while varying the array lattice, particularly in the case of irregular or sparse lattices and complex elements requiring dense meshes in full-wave simulators. The applications of the method may thus range from the systematic analysis of MC to optimization and synthesis.

On the spherical expansion for calculating the sound radiated by a baffled circular piston

An efficient and accurate method for calculating the sound radiated by a baffled circular rigid piston is using spherical harmonics, and the solution is a series containing the integral of spherical Bessel functions. The integral is usually calculated with the generalized hypergeometric functions in existing literatures, which shows poor convergence at middle and high frequencies due to the overflow and the loss of significant figures. A rigorous and closed form solution of the integral is derived in this paper based on the recurrence method, which is accurate in the whole frequency range and thousands of times faster than the existing methods. It is shown that the proposed method can be extended for the calculation of the sound radiated by a baffled piston and an unbaffled resilient disk with axisymmetric velocity and pressure profiles, respectively, and some baffled rotating sources where the velocity profile is asymmetric.

Undrained cylindrical and spherical cavity expansion in elastic–viscoplastic soils

Various undrained cavity expansion solutions for elastic–plastic soil have been proposed previously. However, no solution has been presented for elastic–viscoplastic (EVP) soil until now. This paper presents a general solution method for solving the classical one-dimensional (1D) boundary value problem (BVP) for undrained cylindrical or spherical cavity expansion in EVP soil with an emphasis on the rate effect of soil. The solution method is summarized as three standard procedures: (i) obtaining the soil displacement and strain under incompressible conditions, (ii) calculating the effective stress of soil through a suitable constitutive law, and (iii) obtaining the pore pressure by numerically solving the stress equilibrium equation through the finite difference method (FDM) or other numerical solution techniques. The numerical algorithms for calculating the effective stress and pore pressure are very simple, without any complex iteration processes, and they require little calculation time but provide high computational accuracy. In addition, some numerical results are given to investigate the influence of the cavity expansion velocity on the cavity expansion response. The proposed solution procedure is general and can be applied not only for the EVP model but also for other plasticity models, and the given EVP solution can be applied to interpret the rate effect of the cone penetration test and pile penetration.

Temperature and Metallicity Gradients in the Hot Gas Outflows of M82

Abstract We utilize deep Chandra X-ray Observatory imaging and spectra of M82, the prototype of a starbursting galaxy with a multiphase wind, to map the hot plasma properties along the minor axis of the galaxy. We extract spectra from 11 regions up to ±2.5 kpc from the starbursting midplane and model the data as a multitemperature, optically thin thermal plasma with contributions from a nonthermal (power-law) component and from charge exchange (CX). We examine the gradients in best-fit parameters, including the intrinsic column density, plasma temperature, metal abundances, and number density of the hot gas as a function of distance from the M82 nucleus. We find that the temperatures and number densities of the warm–hot and hot plasma peak at the starbursting ridge and decrease along the minor axis. The temperature and density profiles are inconsistent with spherical adiabatic expansion of a super-heated wind and suggest mass loading and mixing of the hot phase with colder material. Nonthermal emission is detected in all of the regions considered, and CX comprises 8%–25% of the total absorption-corrected, broadband (0.5–7 keV) X-ray flux. We show that the abundances of O, Ne, Mg, and Fe are roughly constant across the regions considered, while Si and S peak within 500 pc of the central starburst. These findings support a direct connection between the M82 superwind and the warm–hot, metal-rich circumgalactic medium (CGM).

Solution for spherical cavity expansion in state-dependent soils

This work presents a spherical cavity expansion solution aimed at linking soil constitutive behavior with quantities that bear direct engineering meanings for practicing engineers (e.g., foundation bearing capacity). For this purpose, we derive the solution based on the state-dependent, critical state constitutive model proposed by Li and Dafalias (Geotechnique 50(4): 449–460, 2000), whose ability to realistically represent the actual mechanical behavior of sand has been extensively verified in the literature. To ensure the reliability of the solution, we verify it against an independent finite element analysis of spherical cavity expansion in solid governed by the same constitutive model. In this validation, we also highlight the dependence of cavity expansion response on the current state of granular materials relative to critical state. The application of the proposed solution in solving engineering problems is demonstrated in predicting the resistance of cone penetration and the ground movements associated with static pipe bursting in sand. We show that, based on the soil parameters determined from laboratory triaxial tests, the proposed solution can reasonably represent the dependence of cone penetration resistance on the density and pressure level of sand, as revealed from centrifuge testing. By comparing with finite element analysis, we demonstrate that the proposed solution can provide useful estimations for soil displacements caused by pipe bursting operation. These archetypal examples suggest that the proposed cavity expansion solution can form a theoretical basis for linking fundamental soil properties with quantities that have direct implications for geotechnical engineering practice.

Undrained shear strength assessment using piezocone and shear wave measurements

In this paper, a new approach is proposed to determine the undrained shear strength of intact clays using the undrained rigidity index inferred from piezocones and shear wave velocity measurements based on the theory of spherical cavity expansion. The derived cone factors are further simplified for young, uncemented (non-structured) clays to be solely expressed in terms of the cone behaviour type index. Moreover, an empirical expression is suggested to relate the undrained shear strength of fissured clays to the cone and shear wave measurements. The proposed approach is used to assess the values of undrained shear strengths in several well-reported test sites. The estimated strengths are found to be in a good agreement with the related field and laboratory measurements in intact clays, whereas in fissured clays, the estimated undrained strengths are shown to match less favourably with the laboratory measurements. This may be attributed to the strong dependence of the undrained shear strength of such clays on the site-specific orientations and properties of the prevailing fissures.

Influence of the mushroomed projectile's head geometry on long-rod penetration

Self-sharpening has been observed in experiments and simulations of long-rod penetration. Penetration performances are influenced by different nose shapes occurred in the penetration of long rods made by different materials. In this paper, to model this nose shape effect, the resistance of the target in the standard Alekseevskii-Tate model is replaced by the resistance determined by the spherical cavity expansion approximation for general nose shapes. The function of nose shape is constructed to establish a modified model of long-rod penetration, in which the nose geometry during the long rod penetration is represented by two main parameters, i.e., the diameter ratio of rod nose and shank η and the nose shape factor N*. The influences of η and N* on long-rod penetration and their mechanisms are analyzed. The penetration performance decreases with an increasing diameter ratio η, whose physical basis is the increased radial flow of rod material around the nose, which in turn, leads to the loss of kinetic energy due to larger cavity formed in the targets. The nose shape factor N* reflects the sharpness of nose shapes, and a smaller value of N* corresponds to a sharper nose. N* obviously affects the ballistic performance of long-rod penetration, however, depending on the initial impact velocity. In general, the influence of N* is relatively smaller than that of η.

Statistical hadronization model for heavy-ion collisions in the few-GeV energy regime

We show that the transverse-mass and rapidity spectra of protons and pions produced in Au-Au collisions at sqrt(sNN) = 2.4 GeV can be well reproduced in a thermodynamic model assuming single freeze-out of particles from a spherically symmetric hypersurface. This scenario corresponds to a physical picture used by Siemens and Rasmussen in the original formulation of the blast-wave model. Our framework modifies and extends this approach by incorporation of a Hubble-like expansion of QCD matter and inclusion of resonance decays. In particular, the Delta(1232) resonance is taken into account, with a width obtained from the virial expansion. Altogether, our results bring evidence for substantial thermalization of the matter produced in heavy-ion collisions in a few GeV energy regime and its nearly spherical expansion.