Equations of State in Soil Compression Based on Statistical Mechanics

Fukue, Masaharu; Mulligan, Catherine N.

doi:10.3208/sandf.49.99

Cited by 7 publications

(3 citation statements)

References 34 publications

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“…Order and probability are concepts joined by entropy. Boltzmann (1898) [7,6] proposed that the entropy relates to the number of possible microstates Ω in the way 3 :…”

Section: Energy and Entropymentioning

confidence: 99%

“…Although today is still a pipe dream finding a universal constitutive law, some results are starting to do it possible for the simplest media. If there was a reproducible state of equilibrium of every medium, it would be possible to propose an equation of state, rather than a constitutive equation [3,4]. An equation of state is a unique function which relates all the intervening properties of the medium in the equilibrium state.…”

Section: Introductionmentioning

confidence: 99%

“…Unfortunately, the complex nature of granular media does not make it possible to propose a universal “behavior law”, or to establish a simple relationship that includes all the observed features of their behavior, although recent developments are starting to make it possible for the simplest granular media. The key idea is that if there was a reproducible state of equilibrium of every medium, it would be possible to propose an equation of state, rather than a constitutive equation (Fukue and Mulligan, 2009; Tejada and Jimenez, 2010). An equation of state is a unique function that relates all the properties intervening in the equilibrium state.…”

Section: Introductionmentioning

confidence: 99%

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Statistical mechanics as guidance for particle‐based computational methods

Tejada

Jimenez

2013

Engineering Computations

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Particle-based methods apply some laws of Classical Mechanics to all the particles of a granular system. On the other hand, classical Statistical Mechanics deals with systems consisting of a lot of particles, focusing on the statistical distribution of some intensive properties. Consequently, the macroscopic behaviour and the average properties of the system in equilibrium are based on some microscopic considerations. To do that, statistical tools and mechanical laws are used together. For an implemented particle-based method to be realistic enough, then the obtained simulations should satisfy some basic underlying physical requirements, and Statistical Mechanics is a useful tool to establish such requirements. This paper presents some results based on Statistical Mechanics that are useful for a realistic modelling of granular systems using Particle-based methods. Examples of the discussed issues include that the same protocol makes a disordered granular medium attain always the same packing ratio; that some local arrangements are less probable than others; that there is a well-established limit to the achievable density of granular assemblies of hard spheres; and that the equilibrium of disordered granular systems does not coincide to the state of minimum potential energy (which would be get in a completely ordered arrangement). The consideration of such issues in practical applications could be helpful to save time in computational methods, to avoid mistakes or, at least, to verify that the implementations are realistic.

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“…Order and probability are concepts joined by entropy. Boltzmann (1898) [7,6] proposed that the entropy relates to the number of possible microstates Ω in the way 3 :…”

Section: Energy and Entropymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Statistical mechanics as guidance for particle‐based computational methods

Tejada

Jimenez

2013

Engineering Computations

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Estimation of the compression behaviour of reconstituted clays

Liu

Zhuang

Horpibulsuk

2013

Engineering Geology

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The void index is a relative quantity measuring the position of the current void ratio of a clay against the void ratios of the clay at two specific vertical effective stresses (i.e., σ v ′ = 100 kPa and σ v ′ =1000 kPa). Based on this concept, a simple systematic tool is proposed for estimating the compression behaviour of reconstituted clays over a wide range of stresses and water contents. Following the practice of geotechnical engineering computation, the compression behaviour of clays is idealised as linear segments in the Iv ~ lnp′ (or the void index and the mean effective stress) space. Considering the variation in the available data, there are three related but independent models for describing the compression behaviour of reconstituted clays. The accuracy of estimation increases with the level of available data. The proposed estimation is used to simulate the behaviour of a variety of reconstituted clays over a wide range of stresses and water contents. With different levels of available data, the estimation is evaluated on the basis of these simulations. The proposed estimation can take maximumuse of available data and provide a simple yet practical tool for calculating the compression behaviour of reconstituted clays and a basic parameter for geotechnical engineering computations, the compression index. An empirical equation for the initial compression index is also suggested and verified. ABSTRACT 61The void index is a relative quantity measuring the position of the current void ratio of a clay 62 against the void ratios of the clay at two specific vertical effective stresses, i.e.,  v = 100 kPa 63 and  v = 1000 kPa.). Based on this concept, a simple systematic tool is proposed for 64 estimating the compression behaviour of reconstituted clays over a wide range of stresses and 65 water contents. Following the practice of geotechnical engineering computation, the 66 compression behaviour of clays is idealised as linear segments in the I v ~ lnp (or the void 67 index and the mean effective stress) space. Considering the variation in the available data, 68 there are three related but independent models for describing the compression behaviour of 69 reconstituted clays. The accuracy of estimation increases with the level of available data. The 70 proposed estimation is used to simulate the behaviour of a variety of reconstituted clays over 71 a wide range of stresses and water contents. With different levels of available data, the 72 estimation is evaluated on the basis of these simulations. The proposed estimation can take 73 maximum use of available data and provide a simple yet practical tool for calculating the 74 compression behaviour of reconstituted clays and a basic parameter for geotechnical 75 engineering computations, the compression index. An empirical equation for the initial 76 compression index is also suggested and verified. 77

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