Journal of Engineering Mechanics

Within a micromechanical framework, a constitutive model for sand capable of predicting noncoaxiality between stress and strain increments is presented. Anisotropy of elastic and plastic material properties is considered by introducing fabric-like second-order coefficient tensors that arise from a description of the interparticle contacts of sand grains. Strength anisotropy is further accounted for by introducing an interlocking parameter that describes the relative ease of sliding depending on the orientation of potential failure planes. The model is calibrated to and validated against two sets of hollow cylinder triaxial compression experiments consisting of various orientations of major principle stress directions, including tests conducted with the principle stress axes noncoaxial with the material axes. Model predictions of noncoaxiality between stress and strain increments are examined and compared with laboratory measurements. The results show that by considering the arrangement of interparticle contacts, the model is capable of predicting such noncoaxiality without the need to specify a priori any assumptions about the noncoaxial behavior.

The structural damage detection (SDD) and on-line integrity assessment is one of the fundamental objectives in the field of structural health monitoring (SHM). Unfortunately, some of the existed SDD methodologies are time-consuming, and more efficient methods are needed as some large complex structures are assessed in practice. In this study, the cloud computing (CC) technology is introduced into the SDD domain for saving the computation cost and for improving the computation efficiency. The CC definition and application are introduced. Then MapReduce is described as its core technology and Hadoop platform adopted as its open source as well. The traditional time series analysis is separated into map and reduce function modules. In combination with the Hadoop, a new CC-based time series analysis method is proposed for SDD by combining CC technology with time series analysis and further by defining damage-sensitive feature (DSF). The performance and efficiency of the proposed CC-based SDD method is assessed by some numerical simulations for single and multiple damages of a two-story rigid frame, further by a series experimental data downloaded from the web site of the Los Alamos National Laboratory (LANL), United States, for damage detection of a three-story building model under the linear and nonlinear damage conditions of structures. The illustrated results show that the new CC-based SDD method can effectively locate the structural damage and quantify the damage severity to some extent. It can save the computation cost and enhance the computing efficiency of SDD implementation. The more the damage cases are, the more significant the speedup ratio is. It is more beneficial to the analysis and processing of the mega data measured on site in the SHM field.

The irregularity of particle motions during quasi-static deformation is investigated using discrete element (DEM) simulations of sphere and sphere-cluster assemblies. A total of three types of interparticle movements are analyzed: relative motions of particle centers, relative motions of material points of two particles at their contact, and the traversal of contacts across the surfaces of particles. Motions are a complex combination of rolling, sliding, and elastic distortion at the contacts, and all motions are highly irregular and variant, qualities that increase with increasing strain. The relative motions of particle centers diverge greatly from those of an affine displacement of the particles. The motions of the nonconvex sphere-cluster particles were more regular that those of the spheres. The paper also investigates the effect of the distance between two remote particles and their pair-wise relative displacements. Even for particle pairs separated by more than six intermediate particles, the relative motions do not conform with the mean deformation (affine) field. Force chains are shown to be transient features, which survive only briefly across elapsed strains.

Numerical simulations, by the discrete element method (DEM), of a model granular assembly, made of spherical balls, are used to investigate the influence of a small amount of an interstitial wetting liquid, forming capillary bridges between adjacent particles, on two basic aspects of granular material rheology: (1) the plastic response in isotropic compression, and (2) the critical state under monotonic shear strain, and its generalization to steady, inertial flow. Tensile strength $F_0=\pi \mathrm{\Gamma }a$, in contacts between beads of diameter $a$ joined by a small meniscus of a liquid with surface tension $\mathrm{\Gamma }$, introduces a new force scale and a new dimensionless control parameter, $P^{*}=a^{2}P/F_0$, for grains of diameter $a$ under confining stress $P$. Under low $P^{*}$, as cohesion dominates, capillary cohesion may stabilize very loose structures. Upon increasing pressure $P$ in isotropic compression, such structures gradually collapse. The resulting irreversible compaction is well described by the classical linear relation between $\log P^{*}$ and void ratio in some range, until a dense structure forms that retains its stability without cohesion as confinement dominates for large $P^{*}$. In steady shear flow, with uniform velocity gradient $\dot{\gamma }=\partial v_1/\partial x_2$ under normal stress $P={\sigma }_{22}$, the apparent internal friction coefficient, which is defined as ${\mu }^{*}={\sigma }_{12}/{\sigma }_{22}$, depends on $P^{*}$ and inertial number (reduced shear rate) $I=\dot{\gamma }\sqrt{m/aP}$, and so does solid fraction $\mathrm{\Phi }$. The material exhibits, as $P^{*}$ decreases, a strongly enhanced resistance to shear (larger ${\mu }^{*}$). In the quasistatic limit, for $I\to 0$, it is roughly predicted by a simple effective pressure assumption by which the capillary forces are deemed equivalent to an isotropic pressure increase applied to the dry material as long as $P^{*}\ge 1$, while the yield criterion approximately assumes the Mohr-Coulomb form. At lower $P^{*}$, such models tend to break down as liquid bonding, causing connected clusters to survive over significant strain intervals, strongly influences the microstructure. Systematic shear banding is observed at very small $P^{*}$.

Deformations in granular media are described by using a representation of the microkinematics of the underlying assembly through Dirichlet tessellation. Based on a probabilistic analysis of topological rearrangements induced by evolving microstructures in the assembly, homogenization is carried out within a multiscale approach—from deforming individual cells to cell network level—to eventually describe global strain in the granular ensemble. In contrast to other models in the literature, tessellation network properties are directly linked to physical microstructural characteristics of the granular assembly through local coordination number and fabric anisotropy. Because these microstructural variables dictate both strain and stress in a granular medium, this provides a route to establish a stress-strain relationship as an ultimate goal. In this paper, detailed attention is paid to the description of evolving fabric anisotropy and coordination number as a combination of dissipative microstructural rearrangements and nondissipative contact losses and gains. By introducing these two mechanisms, peak response of a dense assembly can be modeled as well as asymptotic behavior such as critical state as commonly known in soil mechanics. Model estimates of the response of granular assemblies compare very well with simulation results obtained from discrete element modeling (DEM) computations. Verification was conducted for a wide range of initial density for shearing under both constant mean stress and biaxial compression.

A very limited number of computational studies have been presented for the analysis of the response of saturated granular soils to multidirectional shaking despite it being the realistic mode of loading that resembles an actual earthquake. Herein, this paper examines the capabilities of a recently developed, coupled lattice Boltzmann method (LBM)–discrete element method (DEM) of modeling level and gently sloped soil deposits when subjected to bidirectional shaking. The results of conducted simulations show that bidirectional shaking may increase surface settlement of level deposits by about 30% over unilateral shaking. The depth along the deposit that experiences excess pore pressure ratio close to unity increases as a result of bidirectional shaking compared to unilateral shaking. Bidirectional shaking also increases the magnitude of lateral spreading and associated shear strains in sloping deposits. Other aspects of the response include capturing soil dilative behavior and associated temporary increase in soil strength during liquefaction. The increase in soil strength was more pronounced in the case of the sloping deposit. Investigation into fabric evolution during shaking indicates that soil dilation increases the level of anisotropy and the degree of anisotropy postliquefaction increases compared to the preshaking state.

The drag force law acting on a moving circular disk in a two-dimensional granular medium is analyzed based on the discrete element method (DEM). It is remarkable that the drag force on the moving disk in moderate dense and pure two-dimensional granular medium can be well reproduced by a perfect fluid with separation from the surface of the tracer. A yield force, being independent of the moving speed of the disk, appears if a dry friction between the granular disks and the bottom plate exists. The perfect fluidity is violated in this case. The yield force and the drag force diverge at the jamming point.

Discrete simulation and continuum modeling are two competing methods for analyzing the behavior of complex material systems and granular assemblies. In this paper, a two-dimensional (2D) granular micromechanics model for micromorphic media is presented. The granular micromechanics method is enhanced by incorporating nonclassical terms in the kinematics. These include, in addition to the usual macroscale displacement gradient, the fluctuations in displacement gradient and also the second gradient of displacement. Microscopic intergranular force vectors and macroscopic stress tensors conjugate to the kinematic measures are defined, and the macroscopic strain energy density function is set equal to the volume average of grain-pair energies. As a result, continuum stiffness tensors are formulated on the basis of intergranular stiffness coefficients and fabric parameters defining the geometry of grains and their contacts. To demonstrate the applicability of the continuum method, a random granular assembly is analyzed with both the developed model and discrete modeling method. Results of the discrete analysis then are used to identify the macroscale (or continuum) and the microscale (or grain-pair) stiffness coefficients for a randomly generated assembly of disks. Effects of the three kinematic fields, macrodisplacement gradient, fluctuations in displacement gradient, and its second gradient, are compared. It is found that the derived grain-scale stiffness coefficients are not equal to the ones used in the discrete simulation. This implies that the intergranular stiffness coefficients used for continuum modeling do not represent stiffness of an isolated grain-pair, rather they represent a collective behavior from the grain-pair and its surroundings. An advantage of the granular micromechanics method is that the grains locations and their contacts are not needed. Conversely, for discrete modeling, one needs exact data about grains’ positions and contacts in addition to their contact properties, which can be very complicated, perhaps intractable, for real materials and complex grain assemblies.

A novel approach has been developed to predict the mechanical behavior of very coarse granular materials with a constitutive model, which considers both grain breakage and size effect. The behavior of granular assemblies is significantly influenced by particle breakage. A critical-state double-yield-surface model incorporating the change in the critical-state line and in elastic stiffness caused by grain breakage during loading has been adopted. The amount of grain breakage was estimated by extending the size effect theory on individual grains to granular assemblies. The results from earlier studies on granular materials with parallel gradations have been usefully exploited to calibrate and to validate the model. Comparisons between experiments and simulations suggest that this approach can predict the mechanical behavior of very coarse granular materials from test results performed on a finer fraction with a homothetic gradation.

Depending on the rate of external loading, the permeability, and the boundary conditions, different drainage conditions are expected during the loading of sands. These drainage conditions are thus neither fully drained nor fully undrained as usually assumed for saturated soils, which implies simultaneous changes in pore volume and in pore water pressure. For a given material, the transition between contractive behavior (increase of the pore water pressure) and dilative behavior (decrease of the pore water pressure) defines the phase transformation state. It is found that the position of this phase transformation state, which is known to be dependent on the relative density, depends on the rate of dilatancy (${\dot{\epsilon }}_v/{\dot{\epsilon }}_1$) imposed on the sample. Constraining a loose sample to dilate leads to an unstable state earlier than observed during undrained tests. Even dense samples, which do not exhibit a nonlocalized unstable state during undrained tests, are prone to collapse if the rate to dilatancy is high enough.

The behavior of binary granular mixture is studied by the discrete element method. This granular material contains large and small particles that are similar ellipsoids of different sizes. The size ratio of the major-axes of the large and small ellipsoids is 5. Samples of ellipsoids of different particle shapes have been created by pluviation method and the particle growth technique. Segregation is observed in samples prepared by pluviation method but not particle growth technique. Thus, nine very dense samples (≈ the lowest void ratio) with various fine contents (volume fraction of the small ellipsoids) are generated using the particle growth technique. The result indicates that the packing density is a function of particle shape and fine content. These very dense samples are then sheared under drained triaxial compression to very large strain to determine peak shear strength, critical state void ratio, and ultimate shear strength. Peak shear strength is affected more by particle shape than by fine content. The authors found that the effect of particle shape on the material behavior at critical state is not significant. Fine content affects the critical state void ratio but not the shear strength at very large strain.

Force chains within a granular material are the major load carriers responsible for the strength of a material. The authors study the spatial distribution of force chains across length scales in a three-dimensional (3D) assembly of spherical particles subject to simple shear. Specifically, the authors network sets of force chains by basing connectivity on the distance between chain particles. The authors quantify the connectivity of networked force chains at different length scales using ideas employed in landscape ecology. The authors find a geometric transition in force chain connectivity and observe a change in the character of this transition with respect to force chains restricted to the shear band. The spatial distribution of force chains in the shear band exhibits two dominant length scales: force chains are separated by lateral support, on average, by one particle diameter in one direction and two particle diameters in a second direction. The existence of two dominant length scales in the lateral support around those force chains within shear bands suggests improvements to predictive constitutive models by explicitly incorporating such variation in, for example, in-plane and normal to shear directions.

Microscale parameters have significant influence on the macromechanical behaviors of brittle materials in the discrete-element method (DEM). The rational determination of microparameters is still an open problem to model the failure characteristics of brittle materials. In this study, a three-dimensional DEM with bonded-particles is adopted to simulate the failure process of brittle materials. Interparticle friction and softening failure criteria are applied in the DEM simulations. The physical experimental data of sea ice are adopted to calibrate the DEM results. The influences of the interparticle friction coefficient and the bonding strength of bonded particles on the failure processes of sea ice are analyzed with the DEM simulations of the uniaxial compressive and flexural strengths of sea ice. The ratio of uniaxial compressive to flexural strength is used to calibrate the interparticle strengths and friction coefficient of bonded particles in comparison with experimental data. The relationship between interparticle strength and macrostrength are determined based on the DEM results.