Handling of Constraints in Finite-Element Response Sensitivity Analysis

In this paper, the direct differentiation method (DDM) for finite-element (FE) response sensitivity analysis is extended to linear and nonlinear FE models with multi-point constraints (MPCs). The analytical developments are provided for three different constraint handling methods, namely: (1) the transformation equation method; (2) the Lagrange multiplier method; and (3) the penalty function method. Two nonlinear benchmark applications are presented: (1) a two-dimensional soil-foundation-structure interaction system and (2) a three-dimensional, one-bay by one-bay, three-story reinforced concrete building with floor slabs modeled as rigid diaphragms, both subjected to seismic excitation. Time histories of response parameters and their sensitivities to material constitutive parameters are computed and discussed, with emphasis on the relative importance of these parameters in affecting the structural response. The DDM-based response sensitivity results are compared with corresponding forward finite difference analysis results, thus validating the formulation presented and its computer implementation. The developments presented in this paper close an important gap between FE response-only analysis and FE response sensitivity analysis through the DDM, extending the latter to applications requiring response sensitivities of FE models with MPCs. These applications include structural optimization, structural reliability analysis, and finite-element model updating.     

Return Mapping Algorithms and Stress Predictors for Failure Analysis in Geomechanics

Two well-known return mapping algorithms, the closest point projection method (CPPM) and the cutting plane algorithm (CPA), have been analyzed in detail in relation to two classical failure problems in geomechanics, namely, bearing capacity and slope stability. The stability and efficiency of the algorithms have been investigated in relation to two types of stiffness operators, namely, the consistent elastoplastic modulus and the continuum elastoplastic modulus, and two types of stresses prediction strategies, namely, path independent (based on stresses at previous step) and path dependent (based on stresses at the previous iteration). The numerical experiments show that CPPM working with a consistent elastoplastic modulus and a path independent strategy gives the best performance. It was also observed, however, that the CPA with a continuum elastoplastic modulus and path dependent strategy was quite stable and efficient. This latter observation has implications for advanced constitutive modeling since CPA with a continuum elastoplastic modulus avoids the need for evaluation of the second derivatives of the plastic potential function, making it easier to deal with complicated yield surfaces.     

Finite-Element Simulations of Full-Scale Modular-Block Reinforced Soil Retaining Walls under Earthquake Loading

A finite-element procedure was used to simulate the dynamic behavior of four full-scale reinforced soil retaining walls subjected to earthquake loading. The experiments were conducted at a maximum horizontal acceleration of over 0.8 g, with two walls subjected to only horizontal accelerations and two other walls under simultaneous horizontal and vertical accelerations. The analyzes were conducted using advanced soil and geosynthetic models that were capable of simulating behavior under both monotonic and cyclic loadings. The soil behavior was modeled using a unified general plasticity model, which was developed based on the critical state concept and that considered the stress level effects over a wide range of densities using a single set of parameters. The geosynthetic model was based on the bounding surface concept and it considered the S-shape load-strain behavior of polymeric geogrids. In this paper, the calibrations of the models and details of finite-element analysis are presented. The time response of horizontal and vertical accelerations obtained from the analyses, as well as wall deformations and tensile force in geogrids, were compared with the experimental results. The comparisons showed that the finite-element results rendered satisfactory agreement with the shake table test results.     

Two Finite-Element Discretizations for Gradient Elasticity

We present and compare two different methods for numerically solving boundary value problems of gradient elasticity. The first method is based on a finite-element discretization using the displacement formulation, where elements that guarantee continuity of strains (i.e., C1 interpolation) are needed. Two such elements are presented and shown to converge: a triangle with straight edges and an isoparametric quadrilateral. The second method is based on a finite-element discretization of Mindlin’s elasticity with microstructure, of which gradient elasticity is a special case. Two isoparametric elements are presented, a triangle and a quadrilateral, interpolating the displacement and microdeformation fields. It is shown that, using an appropriate selection of material parameters, they can provide approximate solutions to boundary value problems of gradient elasticity. Benchmark problems are solved using both methods, to assess their relative merits and shortcomings in terms of accuracy, simplicity and computational efficiency. C1 interpolation is shown to give generally superior results, although the approximate solutions obtained by elasticity with microstructure are also shown to be of very good quality.     

Probabilistic Stability Analyses of Embankments Based on Finite-Element Method

Conventional limit equilibrium methods are commonly used to assess the stability of embankments. The finite-element method, as an alternative to limit equilibrium methods, is being increasingly used in the deterministic stability analysis of slopes or embankments. In this paper, a practical procedure for integrating the finite-element method and the limit equilibrium methods into probabilistic stability analysis for embankments is presented. The response surface method is adopted to approximate the performance function for the stability problems and the first-order reliability method is used to calculate the reliability index based on an intuitive expanding ellipsoid perspective. The advantages of the response surface method as a bridge between stand-alone numerical packages and spreadsheet-based reliability analysis via automatic constrained optimization are demonstrated and discussed through a hypothetical two-layer slope and an actual case of the James Bay Dykes. The results show the ease and successful implementation of the proposed procedure for reliability analysis of embankments.     

Asymptotic Prediction of Energetic-Statistical Size Effect from Deterministic Finite-Element Solutions

An improved form of a recently derived energetic-statistical formula for size effect on the strength of quasibrittle structures failing at crack initiation is presented and exploited to perform stochastic structural analysis without the burden of stochastic nonlinear finite-element simulations. The characteristic length for the statistical term in this formula is deduced by considering the limiting case of the energetic part of size effect for a vanishing thickness of the boundary layer of cracking. A simple elastic analysis of stress field provides the large-size asymptotic deterministic strength, and also allows evaluating the Weibull probability integral which yields the mean strength according to the purely statistical Weibull theory. A deterministic plastic limit analysis of an elastic body with a through-crack imagined to be filled by a perfectly plastic “glue” is used to obtain the small-size asymptote of size effect. Deterministic nonlinear fracture simulations of several scaled structures with commercial code ATENA (based on the crack band model) suffice to calibrate the deterministic part of size effect. On this basis, one can calibrate the energetic-statistical size effect formula, giving the mean strength for any size of geometrically scaled structures. Stochastic two-dimensional nonlinear simulations of the failure of Malpasset Dam demonstrate good agreement with the calibrated formula and the need to consider in dam design both the deterministic and statistical aspects of size effect. The mean tolerable displacement of the abutment of this arch dam is shown to have been approximately one half of the value indicated by the classical deterministic local analysis based on material strength.     

Observations on Return Mapping Algorithms for Piecewise Linear Yield Criteria

This paper shows that for perfect plasticity, the closest point projection method (CPPM) and the cutting plane algorithm (CPA) for return mapping are exactly equivalent for piecewise linear yield criteria under both associated and nonassociated plastic flow. The paper demonstrates this by presenting closed-form expressions for returned stresses in terms of predicted stresses. A consequence of this exact approach is that the final stresses can be obtained in a single iteration. The equivalence of CPPM and CPA is further demonstrated numerically by comparing five previously published algorithms for return mapping to Mohr–Coulomb in a finite-element analysis of bearing capacity. The analyses also highlight issues relating to singularities that occur at the corners of the Mohr–Coulomb surface. It is shown that many of these problems can be avoided if the return mapping is performed in principal stress space as opposed to general stress space.     

Development of Fabric Constitutive Behavior for Use in Modeling Engine Fan Blade-Out Events

The development of a robust and reliable material model for fabrics used to prevent fan blade-out events in propulsion engines has significant importance in the design of fan-containment systems. Currently, Kevlar is the only fabric approved by the Federal Aviation Administration to be used in fan-containment systems. However, very little work has been done in building a mechanistic-based material behavior model, especially one that can be used to quantify the behavior of Kevlar when subjected to high-velocity projectiles. Experimental static and high strain rate tensile tests have been conducted at Arizona State University to obtain the material properties of Kevlar fabric. In this paper we discuss the development and verification of a constitutive model for dry fabrics for use in an explicit finite-element program. Results from laboratory tests such as tension tests including high-strain rate tests, picture frame shear tests, and friction tests yield most of the material properties needed to define a constitutive model. The material model is incorporated in the LS-DYNA commercial program as a user-defined subroutine. The validation of the model is carried out by numerically simulating actual ballistic tests conducted at NASA-GRC and fan blade out tests conducted at Honeywell Aerospace (Propulsion Engines).     

Simplified Finite-Element Model for Tissue Regeneration with Angiogenesis

A simplified finite-element model for tissue regeneration is proposed. The model takes into account the sequential steps of angiogenesis (neo-vascularization) and wound closure (the actual healing of a wound). An innovation in the present study is the combination of both partially overlapping processes, yielding novel insights into the process of wound healing, such as geometry related influences, and could be used to investigate the influence of local injection of hormones that stimulate partial processes occurring during wound healing. These insights can be used to improve wound healing treatments. The models consist of nonlinearly coupled diffusion-reaction equations, in which transport of oxygen, growth factors, and epidermal cells and mitosis are taken into account.     

Flow Computation and Mass Balance in Galerkin Finite-Element Groundwater Models

In most groundwater modeling studies, quantification of the flow rates at domain and subdomain boundaries is as important as the computation of the groundwater heads. The computation of these flow rates is not a trivial task when a finite-element method is chosen to solve the groundwater equation. Generally, it is believed that finite-element methods do not conserve mass locally. In this paper, a postprocessing technique is developed to compute mass-conserving flow rates at element faces. It postprocesses the groundwater head field obtained by the Galerkin finite-element method, and the calculated flow rates conserve mass locally and globally. The only requirement for the postprocessor to be applicable is the irrotationality of the flow field, i.e., the curl of the Darcy flux should be zero. The accuracy and the mass conservation properties of the new postprocessor are demonstrated using several test problems that include one-, two-, and three-dimensional flow systems in both homogeneous and heterogeneous aquifer conditions.     

Finite-Element Analysis of Helical Piers in Frozen Ground

This paper presents a study of the behavior of helical pier foundations in frozen ground. The scope of the work presented includes developing finite-element analysis (FEA) models that simulate the stress-strain relationships in the pier and in the surrounding frozen soil. The paper also presents the results of the analysis models developed. The FEA computer program ANSYS is used to perform the computations that include three phases: The first phase is related to the instantaneous stability of piers in frozen or thawed soil under applied design loads. The second phase is related to the analysis of the pier strength during installation into frozen ground when the piers need to withstand installation torque and axial loads. The third phase is related to the long-term stability and critical loads of piers owing to creep in frozen soil. The most important finding of the analysis is that the load is not distributed into the frozen ground equally by the helixes of a multi-helix pier; instead, the bottom helix transfers most of the load.     

Using Finite-Element Method to Simulate Wave Transformations in Surf Zone

In this study, a finite element method proposed by Hsu et al. in 2003 is extended to develop a numerical model for the simulation of wave transformation in the surf zone. The governing equation is the elliptic mild-slope equation including the energy dissipation of wave breaking. At the open boundaries with varying depth, the reflected waves caused by shoaling are adopted to the radiation boundary conditions. The rationality of the present numerical model is examined through the cases of offshore parallel breakwater problems. The results of calculation are in good agreement with experimental results.     

Stochastic Finite-Element Approach to Quantify and Reduce Uncertainty in Pollutant Transport Modeling

One of the important issues in simulation of contaminant transport in the subsurface is how to quantify the hydraulic properties of soil that are randomly variable in space because of soil heterogeneity. Stochastic approaches have the potential to represent spatially variable parameters, making them an appropriate tool to incorporate the effects of the spatial variability of soil hydraulic properties on contaminant fate. This paper presents development and application of a numerical model for simulation of advective and diffusive-dispersive contaminant transport using a stochastic finite-element approach. Employing the stochastic finite-element method proposed in this study, the response variability is reproduced with a high accuracy. Comparison of the results of the proposed method with the results obtained using the Monte?Carlo approach yields a pronounced reduction in the computation cost while resulting in virtually the same response variability as the Monte?Carlo technique.     

Influence of Boundary Conditions in a Finite-Element Analysis of River Levees

The effects of boundary conditions on the stability of a river levee built on a low-permeability soil layer overlying a coarse-grained deposit were studied by using the finite-element method (FEM). The FEM analyses could predict stable or unstable levee conditions depending on the assumed distance between the levee and the external boundary of the mesh where the water table was assumed undisturbed. Possible causes of this notable drawback are discussed. The calibration of the numerical seepage model, through a back analysis of piezometer measurements, that could limit the observed boundary effects is suggested.     

Temporal Thermal Behavior and Damage Simulations of FRP Deck

The finite-element method (FEM) has been employed to study the structural behavior of the fiber-reinforced polymer (FRP) bridge deck. The numerical results were verified with the field-test results provided by New York State Department of Transportation. Fully coupled thermal-stress analyses were conducted using the FEM to predict the failure mechanisms and the “fire resistance limit” of the superstructure under extreme thermal loading conditions. Furthermore, damage simulations of the FRP deck as a result of snow and ice plowing process were performed to investigate any possibility of bridge failure after damage occurs. Thermal simulations showed that FRP bridge decks are highly sensitive to the effect of elevated temperatures. The FRP deck approached the fire resistance limit at early stages of the fire incident under all cases of fire scenarios. The damage simulations due to the snow plowing showed minimal possibility of bridge failure to take place under the worst-case damage scenario when the top 5 mm of the FRP deck surface was removed. The results of both phases of simulations provide an insight into the safety and the reliability of the FRP systems after the stipulated damage scenarios were considered. Moreover, this paper provides discussions concerning the recommended immediate actions necessary to repair the damaged region of FRP deck panels and possible use of the bridge after the damage incident.     

Boundary Finite-Element Method Coupling Finite-Element Method for Steady-State Analyses of Dam-Reservoir Systems

The boundary finite-element method (BFEM) is extended for steady-state analyses of dam-reservoir system problems. In this study, the dam is assumed to be rigid and subjected to horizontal ground motions, and the liquid in the reservoir is assumed to be semiinfinite. The semiinfinite reservoir domain is partitioned into two subdomains: a near-field domain and a far-field domain. In it, the near-field domain is modeled by using the finite-element method (FEM), whereas the far-field domain is modeled by BFEM and is treated as a layered semiinfinite fluid domain. A BFEM/FEM coupling procedure is employed to solve the steady-state response of the reservoir. The coupling procedure is easy to implement and suitable for all frequencies, be it real or complex. The BFEM/FEM coupling procedure is validated in the frequency domain. Numerical results that are based on the present procedure are in good agreement with analytical and other available numerical solutions.     

Finite-Element Parametric Study of the Consolidation Behavior of a Trial Embankment on Soft Clay

The paper presents a case study for numerical analysis of the consolidation behavior of an instrumented trial embankment constructed on a soft soil foundation. Details are given to the geological profile, field instrumentation, laboratory test results, and determination of soil parameters for numerical modeling. Embankment settlement is estimated based on one-dimensional consolidation analysis and nonlinear finite-element analysis following Biot’s consolidation theory. Finite-element results are calibrated against the measured field data for a period of more than 3?years. Development and dissipation of excess pore pressure, long-term settlement, and horizontal displacement are predicted and discussed in light of sensitivity of embankment performance to some critical factors through a parametric study.     

Numerical Simulations of Upsetting Process of the Fresh Fiber-Cement Paste

In this paper, first, the technical aspects for applications of finite-element method (FEM) in modeling material forming processes are reviewed, with a final determination of employing the solid formulation explicit finite element code, ANSYS/LS-DYNA, with the arbitrary Lagrangian–Eulerian mesh to simulate upsetting process, which is the uniaxial compression of a cylindrical specimen between two flat platens, of the fresh fiber-cement paste. After combining a previously proposed elasto-viscoplastic constitutive model for the fresh fiber-cement paste into the numerical procedure, satisfactory agreement between experimental and simulated results is observed for the upsetting force-imposed displacement data. The evolution of the deformation within the material flow in the upsetting process is then interpreted based on the calculated results. The study indicates that the present finite-element procedure, as well as the material constitutive model and the boundary condition treatment, are appropriate for modeling the upsetting process of the fresh fiber-cement paste.     

CPT-Based Evaluation of Liquefaction and Lateral Spreading in Centrifuge

Two series of centrifuge model tests were conducted using Nevada sand. Four saturated models placed in a mildly inclined laminar box and simulating a 6-m-thick deposit were shaken inducing liquefaction effects and lateral spreading. The sand was deposited at a relative density, Dr = 45 or 75%; two of the 45% models were subjected to overconsolidation or preshaking. The second series involved in-flight measurements of static cone tip penetration resistance, qc, simulating the standard cone penetration test (CPT) 36-mm cone. Values of qc increased with Dr, overconsolidation, and preshaking. A normalized resistance, qc1N, was assigned to each of the four liquefaction/lateral spreading models. Increases in Dr, overconsolidation, and preshaking decreased liquefaction and ground deformation, but relative density alone captured these effects rather poorly. Conversely, qc1N predicted extremely well the liquefaction and lateral spreading response of the four models, confirming Seed’s hypothesis to explain the success of penetration-based seismic liquefaction charts. The depth to liquefaction measured in the four centrifuge models is consistent with the field CPT liquefaction chart.     

Two Approaches of Finite-Element Modeling of Ballasted Railway Track

Use of a ballast is still popular in railway engineering due to its resilience, relatively low noise, and convenience in construction and maintenance. The ballast layer was modeled with two modeling approaches in this study–continuous elastic solid and spring-connected elements. Two-dimensional finite element models were built. The parameters of ballast layers were correlated between two models to assure comparability. Three levels of vehicle moving speed were analyzed with the models. Significant differences of rail deflection and ballast were found in all speed levels. Vibration spectra were also compared to reveal the characteristics of different finite element models. It was found that the model with spring-connected discrete elements had higher characteristic frequency than the simple ballast model. Increasing speed may significantly increase rail deflections and ballast vibration levels and result in particles movements in the ballast layer. A thorough understanding of model characteristics and engineering problems is crucial to choose the most appropriate model.