Numerical Analysis of Geomaterials within Theory of Porous Media

It is widely accepted that the mechanical behavior of saturated geomaterials is largely governed by the interaction of the solid skeleton with the fluids present in the pore structure. This interaction is particularly strong in quasi-static and dynamic problems and may lead to the catastrophic loss of strength known as liquefaction, which frequently occurs under earthquake loading. In this work, numerical simulations of saturated granular deposits under transient loads are presented to illustrate the performance of a u-p-U finite-element method formulation and the versatility of the numerical implementation. Closed-form solutions based on both a Biot formulation and modern theories of mixtures are compared with numerical results. In addition, centrifuge experimental results are correlated with numerical simulations. A companion paper presents the details of the theoretical formulation and the numerical implementation within the finite-element method.     

In-Plane Nonlinear Buckling Analysis of Deep Circular Arches Incorporating Transverse Stresses

Large discrepancies exist among current classical theories for the in-plane buckling of arches that are subjected to a constant-directed radial load uniformly distributed around the arch axis. Discrepancies also exist between the classical solutions and nonlinear finite-element results. A new theory is developed in this paper for the nonlinear analysis of circular arches in which the nonlinear strain-displacement relationship is based on finite displacement theory. In the resulting variational equilibrium equation, the energy terms due to both nonlinear shear and transverse stresses are included. This paper also derives a set of linearized equations for the elastic in-plane buckling of arches, and presents a detailed analysis of the buckling of deep circular arches under constant-directed uniform radial loading including the effects of shear and transverse stresses, and of the prebuckling deformations. The solutions of the new theory agree very well with nonlinear finite-element results. Various assumptions often used by other researchers, in particular the assumption of inextensibility of the arch axis, are examined. The discrepancies among the current theories are clarified in the paper.     

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.     

Ritz-Based Static Analysis Method for Fiber Reinforced Plastic Rib Core Skew Bridge Superstructure

A Ritz-based static analysis procedure is described for fiber-reinforced plastic, skew bridge superstructure, or deck, with a parallel grid core. This is a simplified analysis method based on a transformed plate formulation and the classical Ritz method. The rib core bridge superstructure, or deck, is idealized as a homogeneous, orthotropic skew plate to which the Ritz method is applied to discretize the resultant, equivalent orthotropic skew plate. Three laminated skew plate examples are presented; the results are compared with finite-element solution to verify the validity of the simplified method. A practical demonstration of a rib core skew bridge superstructure is investigated using the simplified method. The procedure provides a useful analysis tool that can be used in the preliminary design stage without the use of finite-element analysis.     

Shakedown Approaches to Rut Depth Prediction in Low-Volume Roads

Rutting, due to permanent deformations of unbound materials, is one of the principal damage modes of low traffic pavements. Flexible pavement design methods remain empirical; they do not take into account the inelastic behavior of pavement materials and do not predict the rutting under cyclic loading. A finite-element program, based on the concept of the shakedown theory developed by Zarka for metallic structures under cyclic loadings, has been used to estimate the permanent deformations of unbound granular materials subjected to traffic loading. Based on repeated load triaxial tests, a general procedure has been developed for the determination of the material parameters of the constitutive model. Finally, the results of a finite-element modeling of the long-term behavior of a flexible pavement with the simplified method are presented and compared to the results of a full-scale flexible pavement experiment performed by Laboratoire Central des Ponts et Chaussées. Finally, the calculation of the rut depth evolution with time is carried out.     

Unbonded Posttensioned Concrete Bridge Piers. I: Monotonic and Cyclic Analyses

The monotonic and cyclic behavior of a proposed unbonded, posttensioned concrete bridge pier system is studied using finite-element analyses. A procedure to evaluate seismic capacities based on results from the monotonic and cyclic analyses is described in the framework of a two-level approach considering functional- and survival-performance limits. A set of criteria to define functional-and survival-level displacement capacities for the system is developed. The proposed criteria represent improvements over existing criteria in that they are applicable to both conventional reinforced concrete structures and unbonded posttensioned structures. The monotonic and cyclic behavior of prototype single-column pier and two-column bent designs is presented. Monotonic analyses are performed to characterize the stiffness, strength, ductility, and limit-state behavior of these systems. Cyclic analyses are carried out to estimate energy dissipation capacity, residual displacements, and general hysteretic behavior. The influence of the degree of unbonded posttensioning on bridge pier behavior is examined. Using the finite-element results and the proposed criteria, seismic capacities of the prototype bridge pier systems are established.     

Load-Factor Stability Analysis of Embankments on Saturated Soil Deposits

A continuum-based finite-element methodology is established for quantifying the stability of earthen embankments built on saturated soil deposits. Within the methodology the soil is treated as a fluid-solid porous medium, in which the soil skeleton's constitutive behavior is modeled using a smooth elastoplastic cap model that features continuous coupling between deviatoric and volumetric plasticity. In the stability analysis procedure, self-weight of the embankment soils is monotonically increased at rates characteristic of the embankment construction time, until instability mechanisms develop. The transient effects of excess pore pressures and their impact on soil strength are explicitly modeled, allowing for computation of embankment safety factors against instability as a function of construction rate. Details on the proposed method are presented and discussed, including (1) how the construction rate of an embankment can be modeled; (2) how load-based safety factors can differ from resistance-based safety factors; and (3) solved example problems corresponding to a case history of an embankment failure.     

Analysis of Steady Cone Penetration in Clay

In this paper, a novel finite-element procedure is used to analyze steady cone penetration in soils. Although the procedure is, in principle, applicable to clay and sand with any plasticity model, this paper is only concerned with steady cone penetration in undrained clay. The steady-state finite-element analysis focuses on the total displacements experienced by soil particles at a particular instant in time during the cone penetration test. This is possible because, with the steady-state assumption, the time dependence of stresses and strains can be expressed as a space dependence in the penetration direction. As a result, the finite-element solution of steady cone penetration can be obtained in one step. When compared with the strain path method, the present finite-element procedure offers the following advantages: (1) All equations of soil equilibrium are fully accounted for; (2) cone and shaft roughness can be taken into account in a more rigorous manner and, as a result, the sleeve friction ratio can be properly predicted; and (3) the finite-element procedure can be more easily adapted to analyze cone penetration in dilatant soils.     

Cyclic Behavior and Liquefaction of Sand Using Disturbed State Concept

A general constitutive modeling concept called the disturbed state concept (DSC) is developed in this research for the stress-strain and liquefaction behavior of saturated sands. The DSC model is a unified approach and allows hierarchical modeling for options like elastic and elastoplastic responses, microcracking, damage, and softening. The DSC model parameters for saturated Ottawa sand are evaluated using data from multiaxial tests. The model predictions are found to provide satisfactory correlations with the test results. The DSC model with the foregoing parameters is implemented in a nonlinear dynamic finite-element program (DSC-DYN2D). It is used to solve a typical boundary value problem—a shake table test—involving liquefaction behavior. Based on the results, it can be stated that the DSC model is capable of both characterizing the cyclic behavior of saturated sands and identification of liquefaction.     

Macrokinetics of oxidation of porous substances

Summary A procedure is given for calculating the oxidation kinetics of porous materials obeying a parabolic law of oxidation. The procedure is based cn Zel'dovich's theory. The relations obtained for the reagent concentration, the maximum penetration depth, and the total weight gain as functions of time, temperature, and pore structure, afford a qualitative explanation of all the experimentally observed regularities.The method can be used to calculate the kinetics of diffusion saturation of porous substances by the gas phase, and also of chemical precipitation from solution.     

Continuous Relaxation Spectrum for Concrete Creep and its Incorporation into Microplane Model M4

Efficient numerical finite-element analysis of creeping concrete structures requires the use of Kelvin or Maxwell chain models, which are most conveniently identified from a continuous retardation or relaxation spectrum, the spectrum in turn being determined from the given compliance or relaxation function. The method of doing that within the context of solidification theory for creep with aging was previously worked out by Ba?ant and Xi in 1995 but only for the case of a continuous retardation spectrum based on the Kelvin chain. The present paper is motivated by the need to incorporate concrete creep into the recently published Microplane Model M4 for nonlinear triaxial behavior of concrete, including tensile fracturing and behavior under compression. In that context, the Maxwell chain is more effective than the Kelvin chain, because of the kinematic constraint of the microplanes used in M4. The paper shows how to determine the continuous relaxation spectrum for the Maxwell chain, based on the solidification theory for aging creep of concrete. An extension to the more recent microprestress-solidification theory is also outlined and numerical examples are presented.     

Numerical Modeling of Coupled Hygromechanical Degradation of Cementitious Materials

A coupled hygromechanical model for finite-element analyses of structures made of cementitious materials such as concrete or plaster is formulated within the framework of thermomechanics of partially saturated porous media. A multisurface elastoplastic-damage model, formulated in the space of plastic effective stresses, is employed to describe the nonlinear pre- and postfailure material behavior of concrete, taking the degradation of stiffness as well as the growth of inelastic strains as a consequence of the opening of microcracks into account. From relating stress and strain quantities defined on the mesolevel to respective homogenized quantities on the macrolevel, the hygromechanical coupling coefficients are identified. The effect of cracking on the isothermal liquid permeability is also accounted for. As a representative example, a two-dimensional simulation of a base restrained concrete wall subjected to both uniform drying and to rewetting at the foundation is described in the paper.     

Rheological behavior of Al-Cu alloys during solidification constitutive modeling,experimental identification,and numerical study

The rheological behavior of a solidifying alloy is modeled by considering the deforming material as a viscoplastic porous medium saturated with liquid. Since the solid grains in the mush do not form a fully cohesive skeleton, an internal variable that represents the partial cohesion of this porous material is introduced. The model parameters are identified using shear and compressive stress states under isothermal conditions on an Al-Cu model alloy. The model is partially validated with non-isothermal conditions and we complete this study with tensile conditions. Such conditions, when applied on the mush, may lead to severe defects in many casting processes. The model has been implemented into a commercial finite-element code to simulate a tensile test. Comparison with experimental data shows that the model is able to reproduce the main features of a solidifying alloy under tension, although fracture is not directly addressed here. We show that two critical solid fractions must be introduced in the model to account for the rheology: the coherency solid fraction at which the mush acquires significant strength and the coalescence solid fraction at which solid grains start to form solid bridges.     

Prediction of Damage Behaviors in Asphalt Materials Using a Micromechanical Finite-Element Model and Image Analysis

A study of the micromechanical damage behavior of asphalt concrete is presented. Asphalt concrete is composed of aggregates, mastic cement, and air voids, and its load carrying behavior is strongly related to the local microstructural load transfer between aggregate particles. Numerical simulation of this micromechanical behavior was accomplished by using a finite-element model that incorporated the mechanical load-carrying response between aggregates. The finite-element scheme used a network of special frame elements each with a stiffness matrix developed from an approximate elasticity solution of the stress and displacement field in a cementation layer between particle pairs. Continuum damage mechanics was then incorporated within this solution, leading to the construction of a microdamage model capable of predicting typical global inelastic behavior found in asphalt materials. Using image processing and aggregate fitting techniques, simulation models of indirect tension, and compression samples were generated from surface photographic data of actual laboratory specimens. Model simulation results of the overall sample behavior and evolving microfailure/fracture patterns compared favorably with experimental data collected on these samples.     

Damage Detection in Beam Structures Based on Frequency Measurements

Damage detection in vibrating beams, or beam systems, is dealt with in this paper. Damage is represented by a more or less concentrated decrease in stiffness. A linear behavior is assumed before and after the damage. A peculiar aspect of damage detection, at times neglected, is that damage is frequently concentrated in a few zones, albeit unknown, so that only the modification in the characteristics of a few sections or elements needs to be determined. Attention is focused on the basic aspects of the problem, by discussing the amount of frequencies necessary to locate and quantify the damage uniquely. Two different procedures of damage identification are used, which mainly take advantage of the peculiar characteristics of the problem. Cases with pseudoexperimental and experimental frequencies are solved. A generalization of the procedure based on finite-element models, which makes possible the tackling complex structural cases, is illustrated and discussed with some examples.     

Three-Dimensional Nonlinear Analyses of a Metro Tunnel in S?o Paulo Porous Clay, Brazil

Tropical residual clays with a highly porous structure react to the stress changes induced by tunneling in such a way that surface settlements can be larger than crown-level settlements along a tunnel axis. This behavior, which is not readily simulated by most numerical analyses, was also observed in the Paraiso tunnel, built for the S?o Paulo Metro, Brazil. This is a shallow tunnel driven through porous clayey soils by the sequential method. Detailed results of field monitoring are presented and discussed. 3D finite-element analyses that allowed a detailed simulation of the construction sequence have been carried out, considering two distinct constitutive models for the soil: a simple elastic-perfectly-plastic Mohr-Coulomb model, and the elastoplastic model developed by Lade. The results of these analyses are compared with the observed behavior as well as with the results from a plane strain finite-element analysis. It is shown that only the 3D finite-element analysis coupled with the more sophisticated soil constitutive model provides a full reproduction of field performance, with particular relevance for the deformations in the soil mass over the tunnel.     

Poro-Damage Approach Applied to Hydro-Fracture Analysis of Concrete

An approach using mechanics of saturated porous media is presented to model strongly coupled hydromechanical effects in concrete. Fracture mechanisms of the matrix are taken into account by introducing a tensorial damage variable, which makes it possible to describe orthotropic damage states as well as their effects on hydromechanical parameters (permeability and Biot tensor). An experimental procedure, allowing simultaneous control of pore pressure and applied stresses in a concrete specimen, leads to the identification of material parameters introduced in the constitute model. This model is implemented in the finite-element code CASTEM 2000; numerical simulations of a hydraulic fracture test are then performed and show that the damage-dependence of hydraulic parameters has significant influence on the global response of the structure.     

Postbuckling Analysis of Geometrically Imperfect Conical Shells

A suitable postbuckling analysis, based on geometrically nonlinear behavior, is developed for arbitrary imperfect conical shells. The conical shell was chosen as a representative case exhibiting the entire range of sensitivity to imperfection. A general symbolic code (using the MAPLE compiler) was programmed to create the differential operators of the nonlinear partial differential equations, based on Donnell’s type shell theory. The code then uses the Galerkin procedure, the Newton-Raphson and arc-length procedures, and a finite-differences scheme for automatic development of an efficient FORTRAN code. The code is used for parametric study of the nonlinear behavior and yields the sensitivity characteristic for a wide range of cone semivertex angles. A typical nonlinear behavior of a conical shell is investigated. Comparison with a simpler procedure, based on the initial postbuckling analysis (Koiter’s theory), confirms the need for the present more accurate one, especially for shells with prebuckling nonlinear behavior. The present investigation summarizes the sensitivity behavior with respect to imperfection shapes and amplitudes for the entire range of cone semivertex angles.     

Vertical Vibration of a Flexible Plate with Rigid Core on Saturated Ground

In this paper, the vertical vibration of a flexible plate with rigid core resting on a semi-infinite saturated soil is studied analytically. The behavior of the soil is assumed to follow Biot’s poroelastodynamic theory with compressible soil skeleton and pore water, and the response of the time-harmonic excited plate is governed by the classical thin-plate theory. By virtue of the Hankel transform technique, the fundamental solutions of the skeleton displacements, stresses, and pore pressure are derived, and a set of dual integral equations associated with the relaxed boundary and completely drained condition at the soil-foundation contact interface are also developed. These governing integral equations are further reduced to the standard Fredholm integral equations of the second kind and solved by numerical procedures. Comparison with existing solutions for a rigid permeable plate on saturated soil confirms the accuracy of the present solution. Selected numerical results are presented to show the influence of the permeability, the size of the rigid core, and the plate flexibility on the dynamic interaction between the elastic plate with rigid core and the underlying saturated soil.