Large Deformation Finite-Element Analysis of Submarine Landslide Interaction with Embedded Pipelines

Submarine landslides represent one of the most significant geohazards on the continental slope in respect of the risk they pose to infrastructure such as deep water pipelines. A numerical approach, based on the finite-element method but using remeshing, was established in this paper to simulate large flow deformation of debris from a landslide and to quantify the loads and displacements imposed on pipelines embedded in the seabed. A simple two-dimensional elastic perfectly plastic soil model with plane strain conditions was employed in this analysis. The pipeline was restrained by a set of springs so that the load on the pipeline built up to a stable value, representing the limiting load at which the debris flowed over the pipeline. A parametric study was undertaken by varying the pipeline embedment and the relative strengths of the debris and seabed. The analysis results show that the various combinations of soil strength and embedment depth lead to different debris-pipeline movement patterns and consequently lead to rather different magnitudes of the loads imposed on pipelines. The pipeline is subjected to the largest load (an equivalent pressure of 11.5 times debris strength) from the landslide when it rests on the weakest seabed. The pressure is proportional to the debris material strength but varies inversely with the seabed strength for partially embedded pipelines. For all strength combinations, there is a critical embedment depth beyond which the force on the pipeline reduces to a very small magnitude.     

Flow Establishment in Elastic Pipes

The paper addresses the problem of unsteady flow in an elastic pipe, starting from rest and tending towards a turbulent steady state. Careful experiments, involving uncommonly long, smooth-walled conduits, indicate that the hydraulic performance of an elastic pipe is controlled by its finite speed of response to a change in boundary conditions. The actually occurring, pulsatile flow is well described by a water-hammer analysis of the establishment process, but disagrees significantly with theoretical predictions based on assumed conduit rigidity. Flow accelerations, both temporal and convective, are shown to cause a significant increase in the values of the lower-critical Reynolds number of laminar-to-turbulent transition.     

Simple Nonlinear Model for Elastic Response of Cohesionless Granular Materials

A constitutive model based on hyperelasticity is proposed to capture the resilient (elastic) behavior of granular materials. Resilient behavior is a widely accepted idealization of the response of unbound granular layers of pavements, following shakedown. The coupling property of the proposed model accounts for shear dilatancy and pressure-dependent behavior of the granular materials. The model is calibrated using triaxial resilient test data obtained from the literature. A statistical comparison is made between the predictions of the proposed model and a few of the prominent models of resilient response. The proposed coupled hyperelastic model yields a significantly better fit to the experimental data. It also offers a computational efficiency when implemented in a classical nonlinear finite elemental framework.     

Three-Dimensional Elastic Catenary Cable Element Considering Sliding Effect

The nonlinear behavior of cable-supported bridges is governed by the geometric nonlinearity of cables, which is attributable to sag and sliding effects at the saddle. In a cable-stayed bridge with a midspan saddle, and in all suspension bridges, cable sliding can occur at the saddle under extreme forces, such as those caused by an earthquake or typhoon. However, the conventional method of analysis of cable-supported bridges does not consider the effect of cable sliding at the saddle; instead it regards those cables as fixed. This assumption might lead to a misunderstanding of the global structure system. The goal of this study is to develop a three-dimensional (3D) elastic cable finite element that considers the sliding effect and uses a geometric nonlinear cable finite element based on elastic catenary theory. In this study, two types of sliding were considered: the roller sliding condition without friction and the frictional sliding condition. These were formulated to derive the nodal force vectors and tangential stiffness matrices. To validate the proposed 3D cable sliding element, experiments were conducted for both sliding conditions, and results were compared with calculations of the amount of sliding and displacement at the loading point. In addition, a cable-supported structural system was analyzed to investigate the characteristics of a realistic structure with cable sliding. Overall calculations using the 3D cable sliding model were in very good agreement with the measured values.     

Free Vibrations of Cylindrical Storage Tanks: Finite-Element Analysis and Experiments

This note summarizes a theoretical and experimental study undertaken to provide a deeper understanding of the effect of different parameters on the coupled modal characteristics of circular cylindrical tanks. First, the most common case of clamped-free tanks resting on rigid foundations is investigated by using finite-element (FE) modeling and holographic experiments. A good agreement between experimental and numerical results is a basis to draw a number of conclusions. For both tank geometries investigated, the frequencies for modes of circumferential parameter n = 1 (the “beam” modes) are found to be reduced most significantly by the presence of liquid. Very significant dependence of the radial shell mode shapes on the filling ratio is confirmed both by the FE and experimental results. In addition, nonclassical vibration patterns for radial shell modes were extracted numerically and recorded experimentally. Special attention is paid to the pairs of shell modes. Second, the effects of a flexible foundation and axial compression are investigated using holographic interferometry. The modal responses of this shell–liquid system are found to be different from those of the existing theoretical models.     

Continuous Interface Elements Subject to Large Shear Deformations

Abstract: In this paper, an interface or joint subject to large shear deformation is modeled. In the proposed algorithm, continuous interface elements with a finite thickness are reconstructed at every load step based on current interface configuration, by employing the concept of contact band element. Special strain expressions for the continuous interface elements are derived with regard to the characteristics of shear strain concentration along the interface. The elastic cross-anisotropic model with the special Mohr–Coulomb criterion is applied for the continuous interface elements in view of the anisotropy of interface materials. Simulation of a pullout test has shown that large pullout displacement and realistic structure configuration might be effectively modeled and smooth distributions of mobilized shear stresses along the interface and axial forces in the reinforcement can be obtained without any fluctuation for different interface element thicknesses. However, the stress and axial force distributions along the interfaces and the reinforcement, especially near left end of the reinforcement, vary with the interface thickness. It strongly implies that the continuous interface element with an appropriate thickness should be a good choice for a rock interface or joint with fillings in.     

Nonlinear, Large Deformation Finite-Element Beam/Column Formulation for the Study of the Human Spine: Investigation of the Role of Muscle on Spine Stability

A nonlinear, large deformation beam/column formulation is used to model the behavior of the human spine under compressive load. The stabilizing roles of muscles are accounted for using Patwardhan’s assumption that muscles act to direct the load along the tangent of the column. Three aspects of the spinal structure are then investigated. First, we look at the effects of two different assumptions for the action of muscles, leading to significant differences in the spine behavior. Second, the difference in mechanical properties between the vertebrae and the spinal disks is explored. Third, a nonlinear mechanical response of the spinal disk that arises from a two-step hierarchical homogenization technique is used. It is found that these factors have an important influence on the overall behavior of the spine structure. The present formulation offers a versatile model to investigate various features of the human spine, while remaining affordable computationally. It also provides an interesting framework for future multiscale studies of the human spine.     

Upper Bound for Cylinder Movement Using “Elastic” Fields and Its Possible Application to Pile Deformation Analysis

A new upper bound failure mechanism for the problem of rigid cylinder motion is presented. The velocity field associated with the mechanism is derived from a known elastic solution by similitude of the deformation field. The obtained upper bound value is 21% higher than the exact solution. However, the failure mechanism is continuous, involving no discontinuity, not even on the cylinder perimeter. The solution has a certain advantage if one, for example, wishes to combine its mechanism with a strain path approach to investigate the T-bar penetration problem. The absence of discontinuities in the mechanism also allows evolution of deformation under serviceability conditions, by associating a mobilized strength as a function of an average strain. Based on this approach, a load transfer function for lateral loading of piles in an undrained clay is suggested. This load transfer function involves nonlinear scaling of a stress-strain curve obtained from a triaxial compression test. An analytical, closed form, solution is given for the case of a hyperbolic stress-strain curve.     

Deformation and Cracking of Seepage Barriers in Dams due to Changes in the Pore Pressure Regime

A procedure is presented for analyzing postconstruction deformation of seepage barriers due to changes in the pore pressure regime after seepage barrier construction. The procedure uses the changes in pore pressures calculated by finite-element seepage analyses to calculate changes in buoyancy and seepage forces that occur as a result of seepage barrier construction. When the buoyancy and seepage forces are applied to a finite-element soil-structure interaction model, the result is an effective-stress analysis that rigorously models seepage effects. This paper discusses application of the procedure to five dams to calculate postconstruction deformation and stresses in seepage barriers. The results of the analyses indicate that deformation due to pore pressure regime changes is a likely mechanism causing cracking in rigid seepage barriers.     

Coupling of Fluid Flow and Deformation in Underground Formations

The extraction of fluids from deformable underground formations has resulted in surface subsidence above the formation in several field cases. This paper demonstrates the necessity of using the coupled Biot’s equations for deformation-flow problems in deformable fluid-saturated porous media, particularly for problems involving fluid extraction or injection in underground formations. It is shown that it is not possible to decouple the fluid flow and deformation fields from Biot’s theory except for idealized one-dimensional cases where the total stresses are constant and the deformation mode can be assumed. The deficiencies of the uncoupled approach are also shown via an analysis of a case involving production-induced subsidence in a hydrocarbon field. An important prediction of the coupled analysis is the increase of pore pressure above the initial value during continuous withdrawal of fluids from deformable formations.     

Nonlinear Response of Fluid-Filled Membrane in Gravity Waves

This paper describes a time-domain model for the nonlinear response of fluid-filled membranes in gravity waves. A formulation based on the principle of virtual work provides an integral governing equation for membrane deformation that fully accounts for geometric nonlinearity, which is known to be important even for relatively small deformation. The incident wave amplitude and membrane deformation are considered to be small, to allow linearization of the hydrodynamic problems. The potential flows inside and outside the membrane are solved by two boundary element models, which are coupled to the finite element model of the membrane. An iterative scheme based on Newmark’s method integrates the resulting nonlinear equations of motion in time. The computed results for a bottom-mounted fluid-membrane system show favorable agreement with available experimental and numerical data. Membrane geometric nonlinearity increases the system stiffness due to strain-stiffening and gives rise to hysteresis response at some frequencies.     

Development of an Elastoviscoplastic Microstructural-Based Continuum Model to Predict Permanent Deformation in Hot Mix Asphalt

Permanent deformation in hot mix asphalt is caused by a combination of densification (decrease in volume and hence increase in density) and shear deformation. The primary objective of this paper is to develop an elastoviscoplastic model that accounts for the influence of important microstructure properties such as anisotropy and damage on permanent deformation. The model incorporates a yield surface based on the Drucker-Prager function that is modified to capture the influence of stress state on the material response. Also, parameters that reflect the directional distribution of aggregates and damage density in the microstructure are included in this yield surface model. The elastoviscoplastic model is converted into a numerical formulation and is implemented in finite element (FE). The FE model is used in this study to simulate experimental measurements under different confining pressures and strain rates.     

Three-Dimensional Large Deformation Finite-Element Analysis of Plate Anchors in Uniform Clay

Three-dimensional large deformation finite-element (FE) analyses were performed to investigate plate anchor capacity during vertical pullout. The remeshing and interpolation technique with small strain approach was expanded from two-dimensional to three-dimensional conditions and coupled with the FE software, ABAQUS. A modified recovery of equilibrium in patches technique was developed to map stresses after each remeshing. Continuous pullout of rectangular plate anchors was simulated and the large deformation results for strip, circular, and rectangular anchors were compared with model test data, small strain FE results, and plastic limit solutions. Interface conditions of no breakaway (bonded) and immediate breakaway (no tension) were considered at the anchor base. The effects of anchor roughness, aspect ratio, soil properties, and soil overburden pressure were investigated. It was found that the anchor roughness had minimal effect on anchor performance. For square and circular deep anchors under immediate breakaway conditions, the maximum uplift capacity increased with soil elastic modulus, which suggests that lower bound limit analysis and small strain FE analysis may overestimate the capacity. The soil beneath the anchor base separates from the anchor at a certain embedment depth near the mudline, once tensile stresses were generated. The ratio of separation depth to anchor width was found to increase linearly with the ratio of soil undrained shear strength to the product of soil effective unit weight and anchor width and was independent of the initial anchor embedment depth.     

Steady Streaming around a Circular Cylinder near a Plane Boundary due to Oscillatory Flow

Steady streaming due to an oscillatory flow around a circular cylinder close to and sitting on a plane boundary is investigated numerically. Two-dimensional (2D) Reynolds-averaged Navier-Stokes equations are solved using a finite element method with a k-ω turbulent model. The flow direction is perpendicular to the axis of the cylinder. The steady streaming around a circular cylinder is investigated for Keulegan-Carpenter (KC) number of 2 ≤ KC ≤ 30 with a constant value of Stokes number (β) of 196. The gap (between the cylinder and the plane boundary) to diameter ratio (e/D) investigated is in the range of 0.0–3.0. The steady streaming structures and velocity distribution around the cylinder are analyzed in detail. It is found that the structures of steady streaming are closely correlated to KC regimes. The gap to diameter ratio (e/D) has a significant effect on the steady streaming structure when e/D<1.0. The magnitude of the steady streaming velocity around the cylinder can be up to about 70% of the velocity amplitude of the oscillatory flow. One three-dimensional (3D) simulation (KC = 10, β = 196, and e/D = ∞) is carried out to examine the effect of three dimensionality of the flow on the steady streaming. Although strong 3D vortices are found around the cylinder, the steady streaming in a cross section of the cylinder span is in good agreement with the 2D results.     

Pattern of Two-Phase (DNAPL-Water) Flow through Single Fracture under Temporal Evolution of Aperture

Coupling of two-phase flow with mechanical deformation has important applications in many fields, including dense nonaqueous phase liquid (DNAPL)–water transportation through the subsurface. To understand and couple the different processes, numerical model studies are inevitable at all temporal and spatial scales. This study presents the characterization of DNAPL and water flow in a fracture under confining and fluid pressures. A comprehensive and simplified mathematical model and the conditions under which DNAPL will enter an initially water-saturated fracture under deformation are discussed. A numerical model to predict the quantity of each phase of their saturations is developed. The effect of varying confining stresses on the traverse time of DNAPL across a fractured aquitard is studied. The sensitivity analysis for physical and hydraulic properties, such as apertures, fracture inclination, and fluid and confining pressures, are performed and discussed. The temporal evolution of aperture is necessary to know the proper flow pattern of fluids within a fracture in a multiphase system. These studies are relevant for DNAPL trapped in fractures with very small aperture that can bring changes to flow pattern under deformation.     

Analytical Solution for Fluid-Structure Interaction in Liquid-Filled Pipes Subjected to Impact-Induced Water Hammer

In this paper, an analytical solution for the four-equation model describing fluid-structure interaction in liquid-filled pipes subjected to impact-induced water hammer is presented. The analytical solution is derived for the case of both Poisson coupling and junction coupling. The results obtained from the analytical solution are in good agreement with experimental measurements and with numerical solutions determined by the method of characteristics. Taking advantage of the analytical solution, some features of coupled wave propagation are presented and discussed.     

高压水除鳞喷嘴与射流特性的试验研究

在热轧板带生产尤其是薄板坯连铸连轧工艺中 ,除鳞是提高产品表面质量的关键工序之一 ,目前国内外普遍采用高压水除鳞技术。其中除鳞喷嘴的结构直接影响到射流的打击力及其分布形式 ,对除鳞效果起决定性作用。对高压水除鳞喷嘴的结构及其和水射流的特性之间的关系进行了大量的试验研究 ,总结出了射流散射角、喷射宽度方向特性、轴心打击力的变化规律 ,并对喷嘴结构参数的选择提出了见解。     

Comparison between Coupled and Uncoupled Consolidation Analysis of a Rigid Sphere in a Porous Elastic Infinite Space

Linear consolidation analyses are usually treated either by means of Terzaghi-Rendulic uncoupled theory or Biot’s consolidation theory. In this note, the problem of consolidation displacements around an axially loaded sphere was considered. It is demonstrated that both the uncoupled analysis and the coupled analysis give the same governing equation for pore fluid pressure dissipation with time. A simplified procedure for deriving transient strain components is illustrated. A general solution for time-dependent displacements is obtained using uncoupled consolidation analysis. Close agreement is evident between the new approximate uncoupled analysis solution and the existing coupled analysis solution with a maximum error of less than 0.5%.     

Buried Pipelines Subject to Subgouge Deformations

Engineers often model pipe/soil interaction events based on the concept of subgrade reactions originally proposed by Winkler. Engineering models often utilize beam and nonlinear/plastic spring elements to represent pipelines and the surrounding soil medium, respectively. The spring formulations, defining soil resistance to deformations in three-dimensional space, are usually assumed to be independent and the responses are discrete between adjacent soil zones. However, this idealization does not truly replicate a soil medium behavior. This study presents coupled numerical analyses of pipeline for the specific problem of subgouge deformations due to ice gouge events. Three dimensional continuum analyses of coupled pipe/soil/ice keel interaction using an explicit arbitrary Lagrangian finite- element approach were performed. The study compares the continuum finite-element results with Winkler-type analysis for the specific analyzed problem. A Lagrangian adaptive meshing technique was employed to model very large movement and achieves a steady-state condition; and reasonable ice/soil and soil/pipe interaction interfaces are employed. The numerical analysis shows the potential for continuum modeling of pipe/soil interaction events and develops a better understanding of ice gouging and pipe/soil/ice keel interaction.     

Large-Deflection Deformation of Ferromagnetic Plates in Magnetic Fields

Magnetoelastic buckling and postbuckling of ferromagnetic rectangular plates with geometric nonlinearity in magnetic fields are quantitatively investigated in this paper. A numerical program combining the nonlinear finite element method with an iterative method is proposed to solve the twofold nonlinear problem. The numerical results show that the ferromagnetic plate buckles when it is in a transverse magnetic field, and it bends prior to its instability when it is in an oblique magnetic field with tiny incident angle. The deflection pattern of the plates is changed from one-wave to semiwave after they lose stability.