Journal of Multiscale Modelling

Ground settlement can damage light buildings supported by shallow foundations through cracking. The prediction and modeling of tree roots effect on soil water content and consequently the soil settlements needs a comprehensive analysis of the interactions between tree roots, soil, and water. Root water uptake by trees depends on soil conditions, climatic parameters, and vegetation type. A two-dimensional root-water-uptake model is implemented in a fully coupled thermo-hydro-mechanic finite element program, θ-STOCK. Evapotranspiration from the soil surface covered by grasses is calculated using energy balance and water balance on the surface of soil. The tree roots are modeled as sink terms which are distributed vertically for homogeneous canopy such as forests, or laterally in the case of single tree or a row of trees. The distribution of sink term depends of geometry of root zone and type of canopy. Two case studies are used for verification of implemented model by comparing the modeling results with the measured water content reduction in the zones influenced by tree roots. The soil settlements due to these water content reductions are also calculated.

A magnetofluidized bed consists of a bed of magnetizable particles subjected to a gas flow in the presence of an externally applied magnetic field. In the absence of magnetic field, there is a given gas velocity at which naturally cohesive fine particles can form a network of permanent interparticle contacts capable of sustaining small stresses. This gas velocity marks the jamming transition of the fluidized bed. For gas velocities above the jamming transition, the bed resembles a liquid. Below the jamming transition, the bed behaves as a weak solid and it has a nonvanishing tensile strength. In the absence of magnetic field, the tensile strength of the solidlike stabilized bed has its only origin in nonmagnetic attractive forces acting between particles. In the presence of a magnetic field, the gas velocity at the jamming transition and the tensile strength of the bed depend on the field strength as a consequence of the magnetostatic attraction induced between the magnetized particles. In this work we present experimental measurements on the jamming transition and tensile strength of magnetofluidized beds of linearly magnetizable fine powders. It is shown that powders with similar magnetic susceptibility but different strength of the nonmagnetic forces show a different response to the magnetic field. This finding can be explained by the influence of the nonmagnetic natural forces on the network of contacts. Thus, our experimental results reported in this paper reinforce the role of short-ranged interparticle contact forces on the behavior of the system, which contrasts with the usual modeling approach in which the magnetofluidized bed is viewed as a continuum medium and a fundamental assumption is that the fields can be averaged over large distances as compared with particle size.

Evaluation of the poroelastic properties of oil-well cement paste is essential for prediction of the performance of the cement sheath during the life of a well. A multiscale homogenization model is used to evaluate the poroelastic properties of different classes of oil-well cement paste. The model has been calibrated in a previous work based on the results of a laboratory study on a hardened class G cement paste. A hydration model is used to evaluate the volume fractions of different microstructure phases of cement paste based on the chemical composition of clinker and the water-to-cement ratio. Typical chemical compositions of API class A to class H oil-well cements with their corresponding water-to-cement ratios are used to evaluate the poroelastic parameters such as drained bulk modulus, Biot coefficient, Skempton coefficient, etc. The results show that the difference in the chemical compositions of these cements has not an important effect on the variations of the poroelastic properties. Contrarily, the water-to-cement ratio has an important effect on the variations of these parameters.

The behavior of rock masses is influenced by the existence of discontinuities, which divide the rock in joint blocks making it an inhomogeneous anisotropic material. From the mechanical point of view, the geometrical and mechanical properties of the rock discontinuities define the mechanical properties of the rock structure. In the present paper we consider a rock mass with three joint sets of different dip angle, dip direction, spacing and mechanical properties. The dynamic behavior of the discrete system is then described by a continuum model, which is derived by homogenization. The homogenization technique applied here is called generalized differential expansion homogenization technique and has its roots in Germain's (1973) formulation for micromorphic continua. The main advantage of the method is the avoidance of the averaging of the kinematic quotients and the derivation of a continuum that maps exactly the degrees of freedom of the discrete system through a one-to-one correspondence of the kinematic measures. The derivation of the equivalent continuum is based on the identification for any virtual kinematic field of the power of the internal forces and of the kinetic energy of the continuum with the corresponding quantities of the discrete system. The result is an anisotropic three-dimensional Cosserat continuum.

The two-scale elasto-viscoplastic deformation behavior of amorphous polymer was investigated using the large deformation finite element homogenization method. In order to enable a large time increment for the simulation step in the plastic deformation stage, the tangent modulus method is introduced into the nonaffine molecular chain network theory, which is used to represent the deformation behavior of pure amorphous polymer. Two kinds of heterogeneous microstructures were prepared in this investigation. One was the void model, which contains uniformly or randomly distributed voids, and the other was the heterogeneous strength (HS) model, which contains a distribution of initial shear strength. In the macroscopic scale, initiation and propagation processes of necking during uniaxial tension were considered. The macroscopic nominal stress–strain relation was strongly characterized by the volume fraction and distribution of voids for the void model and by the width of the strength distribution for the HS model. Non-uniform deformation behaviors in microscopic and macroscopic scales are closely related to each other for amorphous polymers because continuous stretching and hardening in the localized zone of the microstructure brings about an increase in macroscopic deformation resistance. Furthermore, computational results obtained from the homogenization model are compared to those obtained from the full-scale finite element model, and the effect of the scale difference between microscopic and macroscopic fields is discussed.