Radoslaw L. Michalowski

Strength anisotropy of fiber-reinforced sand

Abstract The contribution of fibers to the strength of fiber-reinforced soils is very much dependent on the distribution of orientation of the fibers. The fibers in the direction of largest extension contribute most to the strength of the composite, whereas the fibers under compression have an adverse effect on the composite stiffness, and they do not produce an increase in the composite strength. Considering a contribution of a single fiber to the work dissipation during failure of the composite, and integrating this dissipation over all fibers in a composite element, a failure criterion is derived for fiber-reinforced sand with an anisotropic distribution of fiber orientation. A deformation-induced anisotropy was detected in experiments. Specimens with initially isotropic distribution of fiber orientation exhibited a kinematic hardening effect. The evolution of fiber orientation in the deformation process was found to have been the cause of the anisotropic hardening.

Limit Analysis and Stability Charts for 3D Slope Failures

The kinematic approach of limit analysis is explored in three-dimensional (3D) stability analysis of slopes. A formal derivation is first shown indicating that, in a general case, the approach yields an upper bound to the critical height of the slope or an upper bound on the safety factor. A 3D failure mechanism is used to produce stability charts for slopes. The slope safety factor can be read from the charts without the need for iterations. While two-dimensional (2D) analyses of uniform slopes lead to lower safety factors than 3D analyses do, a 3D calculation is justified in cases where the width of the collapse mechanism has physical limitations, for instance, in the case of excavation slopes, or when the analysis is carried out to back-calculate the properties of the soil from 3D failure case histories. Also, a 3D failure can be triggered by a load on a portion of the surface area of the slope. Calculations indicate that for the 3D safety factor of the loaded slope to become lower than the 2D factor f...

Flow of granular material through a plane hopper

Abstract This paper presents some experimental results of an investigation of flow patterns of sand in a plane, wedge-shaped hopper model and also an approach to a theoretical description of the discharge process. A non-steady discontinuos velocity field was observed in the experiments. Velocity discontinuities were traced during the process of discharge using the stereophotographic technique. Complementary information about the density variations of the material during discharge was obtained from X-ray pictures and from ultrasonic measurements. Theoretical description of the velocity field is restricted to the advanced flow, which, as demonstrated in the experiments, can be treated approximately as a pseudo-steady process. An approach based upon the plane plastic flow theory of incompressible Coulomb material is applied. The theoretical solution for the velocity field is compared with some of the experimental results.

SOIL REINFORCEMENT FOR SEISMIC DESIGN OF GEOTECHNICAL STRUCTURES

Abstract The kinematic theorem of limit analysis is used to evaluate the amount of reinforcement necessary to prevent collapse of slopes. The results are also applicable to some failure modes of reinforced walls. Calculations were performed assuming uniform and linearly increasing distributions of reinforcement strength through the slope height. The computational results are presented in charts, which can be used in design. The seismic influence is substituted with a quasi-static horizontal force. While such an approach ignores the acceleration history and does not allow any insight into the behavior of a structure, it is being routinely used in practice, and the charts are offered as a design aid to determine the amount or strength of reinforcement. The length of reinforcement was also calculated, based on collapse mechanisms which include rupture in some layers and pull-out in others. It was found that the distribution of reinforcement with variable spacing, to match the triangular distribution of “smeared” strength, is more economical than a uniform spacing. Uniform spacing requires longer reinforcement and larger strength.

Stability Charts for 3D Failures of Steep Slopes Subjected to Seismic Excitation

Design of slopes and analysis of existing slopes subjected to seismic shaking are carried out routinely using approximations of plane strain and substitution of a quasi-static load for the seismic excitation. A three-dimensional (3D) analysis of slopes is carried out, based on the kinematic theorem of limit analysis. A rotational failure mechanism is used with the failure surface in the shape of a curvilinear cone sector passing through the slope toe, typical of steep slopes. A quasi-static approach is used to develop stability charts allowing assessment of the factor of safety of slopes without the need for an iterative procedure. The charts are of practical importance in cases of excavation slopes and whenever a slope is physically constrained, preventing a plane failure.

Effective width rule in calculations of bearing capacity of shallow footings

Abstract The classical solution to the bearing capacity problem predicts the limit load on symmetrically loaded shallow strip footings. A useful hypothesis was suggested by Meyerhof to account for eccentricity of loading, in which the footing width is reduced by twice-the-eccentricity to its ‘effective’ size. This hypothesis sometimes has been criticized as being overconservative. This paper examines Meyerhof’s suggestion and presents the bearing capacity of eccentrically loaded footings calculated using the kinematic approach of limit analysis. It is found that the effective width rule yields a bearing capacity equivalent to that calculated based on the assumption that the footing is smooth. For more realistic footing models and for cohesive soils the effective width rule is a reasonable account of eccentricity in bearing capacity calculations. Only for significant bonding at the soil-footing interface and for large eccentricities does the effective width rule become overly conservative. For cohesionless soils, however, the effective width rule may overestimate the best upper bound. This overestimation increases with an increase in eccentricity. ©

Static Fatigue, Time Effects, and Delayed Increase in Penetration Resistance after Dynamic Compaction of Sands

Dynamically compacted sands often exhibit a drop in cone penetration resistance immediately after compaction, but a gradual increase in the resistance occurs in a matter of weeks and months. An explanation of the former is sought in analysis of the stress state immediately after a dynamic disturbance, and a justification for the latter is found in the micromechanics process of static fatigue (or stress corrosion cracking) of the micromorphologic features at the contacts between sand grains. The delayed fracturing of contact asperities leads to grain convergence, followed by an increase in contact stiffness and an increase in elastic modulus of sand at the macroscopic scale. Time- dependent increase in small-strain stiffness of sand under a sustained load is a phenomenon confirmed by earlier experiments. It is argued that the initial drop in the cone penetration resistance after dynamic compaction is caused by a drop in the horizontal stress after the disturbance. The subsequent gradual increase in the penetration resistance is not a result of increasing strength, but it is owed to the time-delayed increase in stiffness of sand, causing increase in horizontal stress under one-dimensional strain conditions. This process is a consequence of static fatigue at contacts between grains. The strength of sand after dynamic compaction increases as soon as the fabric of the compacted sand is formed and is little affected by the process of grain convergence in the time after compaction. Contact stiffness, with its dependence on static fatigue, holds information about the previous loading process, and it is a memory parameter of a kind; this information is lost after a dis- turbance, such as dynamic compaction, in which new contacts are formed. The scanning electron microscope (SEM) observations, discrete element simulations, and energy considerations are carried out to make the argument for the proposed hypothesis stronger. DOI: 10.1061/ (ASCE)GT.1943-5606.0000611.

Limit analysis in stability calculations of reinforced soil structures

Abstract Stability analyses of reinforced soil structures are traditionally based on limit equilibrium calculations. Results from such analyses are sometimes ambiguous because of different assumptions made in addition to the limit state. It is shown in this paper that these ambiguities can be removed if the kinematic approach of limit analysis is used, in which a rigorous bound to the required strength of reinforcement is sought. The required strength of reinforcement is the strength needed to maintain stability of the structure. Since limit analysis leads to a rigorous bound on the reinforcement strength, limit loads, or a safety factor, the geometry of the failure mechanisms considered can be optimized, so that the best bound is obtained (a solution closest to the exact solution). A dual formulation of kinematic limit analysis is possible in terms of limit force equilibrium, but the former is preferable since the kinematics of collapse mechanisms appeals to engineering intuition more than the distribution of forces does.

Limit analysis of quasi-static pyramidal indentation of rock

Abstract An approximate analysis of pyramidal indentation into a rock is presented in which the upper bound approach of limit analysis is utilized. The rock is assumed to obey the Mohr-Coulomb yield condition with a small tension cut-off. Two kinematically admissible mechanisms of possible deformation processes, based upon the non-associated flow rule, are adopted for predictions of geometrical variations. The phenomena experimentally observed in rocks, such as dilatancy and deterioration of strength while undergoing deformation, are accounted for approximately in the analysis. The kinematical approach of limit analysis to the problem of block-splitting under pyramidal indentation is also presented in the paper. A number of possible failure modes are examined and those which give the least upper splitting force are shown in detail. Although the particular soluions presented have limited engineering capacity, the method proposed in the paper may find application in solving many rock engineering problems related to drilling, tunnelling, excavating, etc.

Displacement charts for slopes subjected to seismic loads

Abstract Earthquake events in recent years have brought about renewed interest in analyses of slopes subjected to seismic loads. These loads have been accounted for traditionally by using quasi-static loads. Such analyses do not provide any information about permanent displacements, and they neglect the history of seismic shaking. The analysis presented in this note is based on the rigid block displacement technique. A rotational mechanism of slope failure, caused by horizontal shaking, is considered. Yield accelerations are calculated for uniform slopes, and irreversible displacements are calculated for different earthquake records. The displacements can be represented as the product of a coefficient characteristic of a given collapse mechanism and a double time integral of an earthquake acceleration record. Charts are produced to make the application of the results effortless.