Constitutive Sand Model under Undrained Monotonic Loading by Considering Sratio

Modeling of the soil behavior subjected to monotonic loading is of great importance. In traditional old models, incapability of modeling sand strength and subsequently calculation errors lead to unreal definition of sand strength. Furthermore, these models define samples of a soil with different densities and mean stresses as different soils and there is no comprehensive control on state changes during the loading. On the other hand, more advanced models are complicated caasing some problems in their usage. Thus, the necessity of a noble plain model which allows quick and applicable calculations is apparent. In this article sand behavior subjected to monotonic undrained loading is defined from loose state to dense state. In general all stress paths of monotonic loading of a sand in total ranges of confining stress and density throughout confining stress-shear stress space pq and in axial strain-confining stress space å1-p are comparable. Consequently monotonic sand behavior under shear condition can be defined in a new space by means of some state parameters. For this purpose, two new state parameters are presented as: confining stress ratio Rp=p/p0 and shear stress ratio Rs=q/qa. Moreover state pressure index Ip=p/pc is benefited in which p is current confining stress, p0 is initial confining stress, q is current shear stress and pc is critical state confining stress. Due to constant void ratio in undrained test, shear strength of sand is a function of confining stress. Thus by selecting an arbitrary amount of confining stress ratio in stress path prior to phase transformation point, Rpa, corresponding shear stress of Rpa is determined for all stress paths. This shear stress of each stress path is called qa. To characterize the effect of density and density dependent effect of confining stress on shear strength, two spaces å1-Rp and Rp-Rs are considered. Stress paths vary by the flux in initial state pressure index IP0 which lead to form a group of stress paths. In å1-Rp spaces, stress-strain paths are capable of being divided into two distinct groups of paths with 1) IP0≥1 and 2) IP0<1. In Rp-Rs spaces, stress paths with a same void ratio are in a same envelope. Each envelope of stress path is defined as a function of void ratio. In order to investigate effect of IP0 on sand behavior during strain increase, in a quantitative form, diagrams of IP0-Rp are introduced. A diagram of IP0-Rp is defined by determining IP0 of each stress path, in a same level of strain, and diagram of IP0-Rp is achieved for that level of strain. Other diagrams are determined using the same way. Diagrams of Rp-Rs are appropriately capable of indicating the effect of IP0 on sand, and the twoimportant factors controlling their variation are IP0 and void ratio. Subsequently, a relation between confining stress ratio, strain and IP0 and a relation between shear stress ratio, confining stress ratio and void ratio are developed in the form of a model. A simulation of the developed model is performed and employed to investigate the behavior of two different types of sands using two different types of loadings, stress controlled and strain controlled. The obtained results of the model are in good agreements with the available valid laboratory results, which show its capability in defining sand behavior under undrained condition. This model provides a definition of a sand behavior by some specified constants and softening and hardening behavior, and dilative and contractive soil response during loading process, is described in all ranges of density and stresses within the framework of this model.