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An important concern in rock mechanics is non-homogeneity as joints or fault. Adopting the joints as fractures, fractures are well known for their effects on the mechanical and transport properties of rock. It has been postulated that through fractured/jointed rock, mainly, the polygons turned to the shear vector (ti) are involved in the mobilization of shear resistance. Consequently, in order to locate the contact areas implicated into the shear-test it was firstly necessary to fix the shear direction. Moreover, since laboratory observations clearly show that only the steepest polygon surfaces touch the other sample, the identification of the potential sliding areas only requires the determination of the polygons which are faced to the shear direction and which, among them, are steep enough to be involved. The methodology to be discussed here is modeling of slip on the local and global levels due to the distribution of deformation procedure of the rock joint. Upon the presented methodology, more attention has been given to slip initiation and propagation through rock joint. In particular, softening in non-linear behaviour of joint in going from the peak to residual strengths imparts a behaviour often associated with progressive failure. A multi-plane based model is developed and used to compute plastic strain distribution and failure mechanism of rock joints. Validity of the presented model was examined by comparing numerical and test results showing the behavior of both homogeneous and jointed rock samples under general stress conditions.

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Analysis and prediction of structural response to static or dynamic loading requires prediction of concrete response tovariable load histories. The constitutive equations for the mechanical behavior of concrete capable of seeing damage effects or crack growth procedure under loading/unloading/reloading was developed upon micro-plane framework. The proposed damage formulation has been built on the basis of five fundamental types of stress/strain combinations, which essentially may occur on any of micro-planes. Model verification under different loading/unloading/reloading stress/strain paths has been examined. The proposed model is capable of presenting pre-failure history of stress/strain progress on different predefined sampling planes through material. Many of mechanical behavior aspects happen during plasticity such as induced anisotropy, rotation of principal stress/strain axes, localization of stress/strain, and even failure mechanism are predicted upon a simple rational way and can be presented.

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A framework for development of constitutive models including damage progress, based on semi-micromechanical aspects of plasticity is proposed for concrete. The model uses sub-loading surface with multilaminate framework to provide kinematics and isotropic hardening/softening in the ascending/descending branches of loading and can be able to keep stress/stain paths histories for each plane separately. State of stresses on planes is divided to four basic stress patterns i.e. pure compression, increasing compression-and shear, decreasing compression-shear and tension-shear and used in derivation of plasticity equations. Under this kind of categorized form the model is capable of predicting behavior of concrete under any stress/strain path such as uniaxial, biaxial and triaxial in the monotonic and cyclic loading, Also this model is capable of predicting the effects of principal stress/strain axes rotations and consequent plastic flow and has the potential to simulate the behavior of material with anisotropy, fabric pattern, slip/weak planes and crack opening/closing. The material parameters of model are calibrated by optimum fitting of the basic test data available in the literature. The model results under both monotonic and cyclic loading have been compared with experimental results to show capability of model.

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Concrete is a heterogeneous material with a highly non linear behavior, which is mainly caused by the

initiation and propagation of micro cracks within the several components of the material. The damage behavior of

concrete is usually simulated on the macro scale using complex constitutive models. The direct determination of the

homogenized material parameters is often difficult and sometimes impossible. Furthermore these materials models do

not explicitly represent effects and bond behaviors of interfaces between the several components. So in order to predict

of concrete behaviors and characteristics, it should be modeled as a three phase composite material consisting of

aggregate, interfacial transition zone (ITZ) and cement paste. The size and distribution of aggregate affects concrete

characteristics. Because of the random distribution and size variation of aggregate in concrete, the modeling of

concrete behavior based on component in meso structure is difficult and so we must use simple assumption. In this

paper with mixing design and grading curve we developed a simple method to replace real aggregate with equivalent

sphere aggregate with effective diameter. So we can use simple methods instead of complex numeral and randomness

or x ray methods to find effective diameter and use it to determine two arrangements with maximum and minimum

aggregate volume as a repeatable basical element .As a result we can use this element to modeling the behavior of

sample concrete in meso scale and three phases.

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Large size direct shear tests (i.e.300 x 300mm) were conducted to investigate the interaction between clay reinforced with geogrids embedded in thin layers of sand. Test results for the clay, sand, clay-sand, clay-geogrid, sandgeogrid and clay-sand-geogrid are discussed. Thin layers of sand including 4, 6, 8, 10, 12 and 14mm were used to increase the interaction between the clay and the geogrids. Effects of sand layer thickness, normal pressure and transverse geogrid members were studied. All tests were conducted on saturated clay under unconsolidated-undrained (UU) conditions. Test results indicate that provision of thin layers of high strength sand on both sides of the geogrid is very effective in improving the strength and deformation behaviour of reinforced clay under UU loading conditions. Using geogrids embedded in thin layers of sand not only can improve performance of clay backfills but also it can provide drainage paths preventing pore water pressure generations. For the soil, geogrid and the normal pressures used, an optimum sand layer thickness of 10mm was determined which proved to be independent of the magnitude of the normal pressure used. Effect of sand layers combined with the geogrid reinforcement increased with increase in normal pressures. The improvement was more pronounced at higher normal pressures. Total shear resistance provided by the geogrids with transverse members removed was approximately 10% lower than shear resistance of geogrids with transverse members.

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A semi-micromechanical multilaminate model is introduced here to predict the mechanical behavior of soils.

This model is like a bridge between micro and macro scale upon the satisfaction of minimum potential energy level

during any applied stress/strain increments. The concept of this model is based on a certain number of sampling planes

which constitute the elastic-plastic behavior of the soil. The soil behavior presents as the summation of behavior on

these planes. A simple unconventional constitutive equations are used in each of the planes to describe the behavior

of these planes separately. An unconventional plasticity can predict the soil behavior as a smooth curve with

considering plastic deformation due to change of stress state inside the yield surface. The model is capable of

predicting softening behavior of the soil in a reasonable manner due to using unconventional plasticity. The influences

of induced anisotropy are included in a rational way without any additional hypotheses owing to in-nature properties

of the multilaminate framework. Results of this model are compared with test data and reasonable agreement is found.

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The present paper is devoted to a new critical state based plasticity model able to predict drained and undrained behaviour of

granular material. It incorporates a bounding surface plasticity model describing in multilaminate framework to capitalize on

advantages of this mathematical framework. Most of the models developed using stress/strain invariants are not capable of

identifying the parameters depending on directional effects such as principal stress rotation and fabric this is mainly because

stress/strain invariants are scalar quantities. The principal features of this model can be postulated as considering both inherent

and induced anisotropy, principal stress rotation. Since the local instability of saturated sand within post-liquefaction is highly

dependent on the residual inherent/induced anisotropy, bedding plane effects and also the stress/strain path the new mode is

competent to be employed in this regard. The constitutive equations of the model are derived within the context of non-linear

elastic behaviour for the whole medium and plastic sliding of interfaces of predefined planes. As follows, the constitutive

equations are described in detail and then the experimental results and sensitive analysis of key material constants are shown

which all imply the power of the model in predicting of soil behaviour under any condition in soil structures.

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An important concern in rock mechanics is non-homogeneity as joints or fault. This noticeable feature of failures in rock is

appearance of slip surfaces or shear bands, the characteristics of that are associated with deformation being concentrated in a

narrow zones and the surrounding material remaining intact. Adopting the joints as fractures, fractures are well known for their

effects on the mechanical and transport properties of rock. A damaged pro-elasticity multi-plane based model has been developed

and presented to predict rock behavior. In this multi-plane model, the stress–strain behavior of a material is obtained by

integrating the mechanical response of an infinite number of predefined oriented planes passing through a material point.

Essential features such as the pro-elasticity hypothesis and multi-plane model are discussed. The methodology to be discussed

here is modeling of slip on the local and global levels due to the deformation procedure of the existing/probable joints of rock and

this method has a potential of using different parameters on different sampling planes to predict inherent anisotropy of rocks.

Upon the presented methodology, more attention has been given to slip initiation and propagation through these joints. In

particular, softening in non-linear behavior of joints in going from the peak to residual strengths imparts a behavior often

associated with progressive failure. The predictions of the derived stress–strain model are compared to experimental results for

marble, sandstone, Quartz mica schist and anisotropic schist. The comparisons demonstrate the capability of this model to

reproduce accurately the mechanical behavior of rocks.