Masanobu Oda

Experimental micromechanical evaluation of strength of granular materials: Effects of particle rolling

Biaxial compression tests have been performed on assemblies of oval cross-sectional rods, in an effort to evaluate the effects of interparticle friction, particle shape, and initial fabric on the overall strength of granular materials. The variation in the spatial arrangement of the particles (fabric) and particle rolling and sliding are monitored by taking photoelastic pictures at various stages during the course of deformation. Based on this, the following conclusions are obtained. (1) Particle rolling appears to be a major microscopic deformation mechanism, especially when interparticle friction is large. (2) There are relatively few contacts at which relative sliding is dominant, and this seems to be true even when the assembly reaches the overall failure state; this observation is in contradiction to the common assumption that particle sliding is the major microscopic deformation mode. (3) During the course of deformation and up to the peak stress, new contacts are continually formed in such a manner that the contact unit normals tend to concentrate more in a direction parallel to the maximum principal compression. This concentration of unit normals seems to be closely related to the formation of new column-like load paths which carry the increasing axial stress under constant lateral force. After the peak stress, such a column-like microstructure disappears and considerable rearrangement of the load paths takes place, leading to a more diffused (homogeneous) microstructure in the critical state. (4) If a fabric tensor Fij, i, j = 1,2,3, is defined to be proportional to the volume average of the quantity mimj, where mi are the rectangular Cartesian components of a unit vector along a vector that connects the centroids of two typical contacting granules, then it appears that the overall stress with components σij tends to become coaxial with the fabric tensor Fij, as the overall deformation continues. For two-dimensional granules the result σij = αOFij + βOFjkFkj (k summed) obtained by Mebrabadi, Nemat-Nasser and Oda (1980) by microchemical modeling is confirmed experimentally; αO and βO are material parameters.

Micro-deformation mechanism of shear banding process based on modified distinct element method

Numerical simulation tests were carried out using the distinct element method (DEM) by paying much attention to the micro-deformation mechanism leading to the development of shear bands. To do this, the conventional DEM was modified slightly such that the effect of rolling resistance at contact points could be taken into account (called MDEM). It is found that MDEM can be a powerful tool for simulating not only the generation of large voids inside a shear band but also the high gradient of particle rotation along the shear band boundaries, in a quite similar manner to those observed in natural granular soils. It is concluded, based on the numerical simulation tests, that the basic micro-deformation mechanism ending up with the formation of shear bands is in the generation of a column-like structure during the hardening process and its collapse in the softening process.

Study on couple stress and shear band development in granular media based on numerical simulation analyses

From the reasonable accordance between the simulation and laboratory tests, it is concluded that the simulation test using the distinct element method can provide a powerful tool to simulate the micro- as well as macro-behavior of granular media. This is true, in particular, when the rotational resistance is introduced into the conventional one. Based on both the simulation and laboratory tests, we reached the following conclusions: One of the most important changes in microstructure, which takes place during a strain hardening process, is the formation of column-like structure growing parallel to the major principal stress direction. After failure, the column-like structure is reconstructed during a strain softening process by means of rolling, not sliding, at contact points so that a high gradient of particle rotation is generated, changing from negative to positive in a relatively narrow shear zone. Large voids appear in the shear band, and the resulting local void ratio can exceed the corresponding maximum one determined by a standard method. This fact strongly suggests that unique stress condition, which leads to such special microstructure, may develop in the shear band. In fact, couple stresses exist in a shear band in a manner consistent with the change of the particle rotation gradient from negative to positive. In spite of the presence of the couple stress, the stress tensor is nearly symmetric, indicating that the couple stress is very small in magnitude. The presence of the small couple stress still plays an important role in the development of microstructure in shear bands.

Damage growth and permeability change in triaxial compression tests of Inada granite

Microcracking (crack growth), along with accumulation of inelastic strain, takes place in crystalline rock such as granite when it is subjected to differential stress. As a result, growing cracks become interconnected, completely altering permeability. Therefore, coupling between crack growth and permeability change must be determined to fully understand the hydro-mechanical response of rocks subjected to non-hydrostatic stress. Damage growth in triaxial tests on Inada granite under confining pressures up to 140 MPa was analyzed using the crack tensor concept proposed by Oda (Soils and Foundations 22 (4) (1982) 96), and permeability change was also formulated in terms of damage growth. Transient pulse tests were carried out on the damaged samples to see if the permeability change is really related to the associated damage growth. The conclusions are summarized as follows: A permeability tensor formulated by microstructural parameters is well supported by the transient pulse tests. This is particularly true when we deal with highly damaged granite. Where crack density is low, however, the hydraulic properties must be considered by taking into account the effect of spherical pores on them. The permeability of the sample subjected to increasing stress up to failure is about two to three orders of magnitude larger than that of intact granite under the same confining pressure (140 MPa). This change is surprisingly large compared with the result by Zoback and Byerlee (J. Geophys. Res. 80 (5) (1975) 752). Permeability tensors of the damaged samples are represented as more or less isotropic tensors. Rocks under stress in the field can be regarded as isotropic porous media, in spite of the fact that cracks grow preferentially parallel to the major stress.

Inherent and induced anisotropy in plasticity theory of granular soils

Abstract Two tensors (called fabric tensors) are introduced to measure the inherent and induced anisotropy for granular materials. These tensors are explicitly used in the framework of soil plasticity. Yield functions dealing with anisotropic soils, for example, are obtained by generalizing any yield function proposed for isotropic soils, where the stress invariants are substituted by the corresponding joint invariants including the fabric tensors. A possible mechanism of hardening (i.e., the evolution rule) is also considered on the basis of new findings on the microscopic change of particle configuration.

Similarity rule of crack geometry in statistically homogeneous rock masses

Abstract An nth rank tensor called the generalized fabric tensor is introduced to express crack geometry due to discontinuities like joints and faults in rock masses. Statistically homogeneous rock masses can be regarded as geometrically similar bodies if they are characterized by a common fabric tensor. In order to say that they are also similar in mechanical properties, the crack geometry must be similar in the sense of the generalized fabric tensor. The generalized fabric tensor can be expressed by (1) the number of cracks crossed by a unit length of a scanning line, (2) the number of cracks associated with a unit area of a scanning plane, and (3) the density function E (n) to describe the orientation of crack normal unit vectors n. Since these are all determined by conventional field surveys, one can say that the similarity rule for crack geometry is ready to be used in practical rock mechanics.

A method for evaluating the effect of crack geometry on the mechanical behavior of cracked rock masses

Abstract Discontinuities like faults and joints (called cracks) are of widespread occurrence in rock masses in situ, with very complicated geological setting. The complexity, especially in their geometry, is no doubt a major obstruction to develop a useful theory for evaluating the mechanical behavior of cracked rock masses. An index measure (called fabric tensor) which has been introduced to show crack geometry is further discussed in this paper to see if it is useful for evaluating the mechanical behavior of rock masses in situ. Based on some acceptable simplification, an overall elastic compliance for cracked materials is successfully formulated in terms of the fabric tensor. Furthermore, with the help of geometrical probability, the fabric tensor is expressed in terms of in situ measurable quantities. These results strongly suggests that the concept of fabric tensor is useful in the analysis of cracked rock masses.

Preferred orientations of open microcracks in granite and their relation with anisotropic elasticity

In order to study how to deal with open microcracks in rock, anisotropic behaviors of Oshima granite were investigated by carrying out wave velocity tests and uniaxial compression tests, together with observations of microcracks under an optical microscope equipped with a universal stage. Anisotropy in the longitudinal wave velocity VL and secant deformation modulus E10 at 10% strength is caused by pre-existing open microcracks, not by pre-existing healed microcracks. The structural anisotropy formed by open microcracks, which is quantitatively represented by a second-rank tensor (called crack tensor), is in good agreement with the directional changes of E10 and VL: The mechanical, as well as structural, anisotropy shows rhombic symmetry with orthogonal symmetry axes in the directions roughly normal to the rift, grain and hardway planes, which are parallel to the major joint sets in the field. Since longitudinal wave velocity changes drastically depending on the density and orientation of open microcracks in granitic rocks, it is suggested that the crack tensor can be determined from non-destructive wave velocity tests. The elastic modulus tensor theoretically formulated in terms of the second-rank crack tensor can be used, as a first-order approximation at least, to describe the anisotropic elasticity of Oshima granite induced by pre-existing open microcracks. It is of particular importance to point out that the micro-scale structure by open microcracks is geometrically similar to the macro-scale structure by joints and faults (scale independent). This finding strongly suggests that some of the conclusions related to open microcracks are applicable to deal with macro-scale cracks in rock masses.

Effects of induced anisotropy on the development of shear bands in granular materials

Microstructural changes during shear deformation in two natural sands and one artificial assembly of oval rods are investigated with special interest in the micromechanisms leading to the generation of shear bands. Anisotropy is gradually apparent, in a strain-hardening process, as load carrying columns develop and extend parallel to the major principal stress direction. Buckling of these columns, which starts near the peak stress, causes strain softening accompanied by the generation of shear bands. As a result, large voids are produced in shear bands between the buckling columns, and the resulting local void ratio can be larger than the maximum void ratio. Particle orientation changes sharply at shear-band boundaries, so that a high gradient of particle rotation can be developed within relatively narrow shear zones during the shear-banding process. Based on these findings, a microdeformation model is proposed, which emphasizes that the development of induced anisotropy in the strain-hardening process is a necessary condition for the generation of shear bands in granular soils.

A crack tensor and its relation to wave velocity anisotropy in jointed rock masses

Abstract Crack geometry, which is closely related to the mechanical anisotropy of discontinuous materials such as rocks and rock masses, can be concisely expressed by a tensor F (called the crack tensor). In order to give a mathematical expression for the change of longitudinal wave velocity with direction, an additional tensor V is introduced. Three examples (gypsum plaster samples with artificial cracks, granites with microcracks and jointed granites) are reported in this paper with the special emphasis on the relation between the crack geometry F and the directional wave velocity V. Both tensors are co-axial in the sense that the major principal axis of F accords well with the minor one of V. The anisotropic change of wave velocity with direction can be associated with the anisotropic index measure for the crack geometry, suggesting a causal relation. Such relations are useful for extracting information concerning the crack geometry of jointed rock masses from geophysical exploration.