Quantum-thermodynamic treatment of intrinsic anharmonicity; Wallace’s theorem revisited

Wallace (in Thermodynamics of crystals, 1972) developed a theorem, rooted in rigid lattice dynamics, which incorporates intrinsic anharmonic effects in solids. The practical application of this theorem in mineral physics is computationally involved and this is the main reason for the theorem not getting the attention it deserves. Because intrinsic anharmonicity is an important issue at the extreme conditions in planetary mantles, we derived a method which removes the computational obstacles in applying this theorem. We extended the theorem to incorporate details of the phonon spectrum and tested our algorithm on forsterite (Mg₂SiO₄). Using a least squares inversion technique applied to all available experimental data, we show that it results in an accurate representation of thermodynamic properties and sound wave velocities of Mg₂SiO₄ in its complete pressure–temperature stability range. We also show that the accuracy of our results is not significantly affected by the use of a different equation of state.     

Analysis of pressuremeter geometry effects in clay using critical state models

The conventional interpretation methods of pressuremeter testing effectively approximate pressuremeter membranes as infinitely long. As a result, the effects of the two‐dimensional geometry of pressuremeters are ignored, leading to an overestimation of soil shear strength by pressuremeter testing, as demonstrated in several previous studies. This paper presents results of a numerical study of two‐dimensional geometry effects on self‐boring pressuremeter tests in undrained clay. The results are obtained using critical state soil models with an effective stress formulation. This is in contrast to most (if not all) existing studies on pressuremeter geometry effects, which were based on perfectly plastic soil models (e.g. Yu (Cavity expansion theory and its application to the analysis of pressuremeters. DPhil Thesis, The University of Oxford, 1990), Yeung and Carter (Proc. 3rd Int. Symp. on Pressuremeters, 1990), and Houlsby and Carter (Géotechnique, 1993; 43 (4):567–576)). The present study suggests that the overestimation of soil strength due to the neglect of finite pressuremeter length is significantly affected by the soil model used in the calculations. It is found that for clays with a high overconsolidation ratio (OCR) the strength overestimation predicted using critical state soil models could be considerably smaller than that predicted using perfectly plastic soil models. The main conclusion of this numerical study is that care must be exercised before directly applying any numerically determined pressuremeter geometry correction factors in practice. Copyright © 2005 John Wiley & Sons, Ltd.     

‘Boundary’ in Ancient Persian Tradition of Statehood

It is universally accepted that the need for defining precise lines of separation and points of contacts between states is the byproduct of the emergence of nation-states and ‘world economy’ in the 19th century Europe. Nevertheless, it is hard to overlook the fact that these modern notions are rooted in periods prior to the emergence in Europe of nation-states. There are indications that ancient civilizations were familiar with the notion of ‘state’ in connection with the concepts of territory and boundary. Ancient texts reveal that this basic principle existed in ancient Persian literature in respect of matters of state, territory, and boundary. Similarly, the likelihood exists that these Persian notions could have influenced Roman civilization. It is widely believed that a combination of ancient Greco-Roman and Persian civilizations is a major contributor to what culturally constitutes ‘West’. Later in the Sassanid period the inter-linked notions of state, territory, and boundary developed substantially, coming quite close to their contemporary forms. On the other hand, considering that ‘justice’ was the corner stone of ancient Persian Political philosophy, the idea that ancient Persian spatial arrangement might have contributed to the evolution of the concept of democracy in the West may not be too difficult to contemplate.     

Generalized plasticity state parameter‐based model for saturated and unsaturated soils. Part 1: Saturated state

The behavior of granular materials is known to depend on its loose or dense nature, which in turns depends both on density and confining pressure. Many models developed in the past require the use of different sets of constitutive parameters for the same material under different confining pressures. The purpose of this paper is to extend a basic generalized plasticity model for sands proposed by Pastor, Zienkiewicz and Chan by modifying the main ingredients of the model flow—rule, loading–unloading discriminating direction and plastic modulus—to include a dependency on the state parameter. The proposed model is tested against the available experimental data on three different sands, using for each of them a single set of material parameters, finding a reasonably good agreement between experiments and predictions. Copyright © 2010 John Wiley & Sons, Ltd.     

Quantifying flows along hydrological pathways by applying a new filtering algorithm in conjunction with master recession curve analysis

Quantifying the proportion of the river hydrograph derived from the different hydrological pathways is essential for understanding the behaviour of a catchment. This paper describes a new approach using the output from master recession curve analysis to inform a new algorithm based on the Lyne and Hollick ‘one‐parameter’ signal analysis filtering algorithm. This approach was applied to six catchments (including two subcatchments of these) in Ireland. The conceptual model for each catchment consists of four main flow pathways: overland flow, interflow, shallow groundwater and deep groundwater. The results were compared with those of the master recession curve analysis, a recharge coefficient approach developed in Ireland and the semi‐distributed, lumped and deterministic hydrological model Nedbør‐Afstrømings‐Model. The new algorithm removes the ‘free variable’ aspect that is typically associated with filtering algorithms and provides a means of estimating the contribution of each pathway that is consistent with the results of hydrograph separation in catchments that are dominated by quick response pathways. These types of catchments are underlain by poorly productive aquifers that are not capable of providing large baseflows in the river. Such aquifers underlie over 73% of Ireland, ensuring that this new algorithm is applicable in the majority of catchments in Ireland and potentially in those catchments internationally that are strongly influenced by the quick‐responding hydrological pathways. Copyright © 2013 John Wiley & Sons, Ltd.     

Limitations of suction‐controlled triaxial tests in the characterization of unsaturated soils

Behavior of unsaturated soils is influenced by many factors, and the influences of these factors are usually coupled together. Suction‐controlled triaxial (SCTX) tests are considered to allow researchers to investigate influences of individual variables on unsaturated soils under specified stress path with controls of stresses, pore water, and air pressures. In the past 50 years, SCTX testing method has been established as a standard approach to characterize constitutive behavior of unsaturated soils. Most important concepts for modern unsaturated soil mechanics were developed upon results from the SCTX tests. Among these, one of the most important contributions in the constitutive modeling of elasto‐plastic behavior for unsaturated soils is the Barcelona basic model (BBM) proposed by Alonso et al. in 1990. The BBM successfully explained many features of unsaturated soils and received extensive acceptance. However, the SCTX tests are designed based upon the divide‐and‐conquer approach in which an implicit assumption is used: soil behavior is stress‐path independent. However, it is well‐established that unsaturated soil behavior is elasto‐plastic and stress‐path dependent. It is found that the SCTX tests in fact cannot control the stress path of an unsaturated soil during loading. This incapability, in combination with complicated loading/collapse behavior of unsaturated soils, makes the SCTX tests for characterizing unsaturated soil questionable. This paper discusses the limitations of the SCTX tests in the characterization of unsaturated soils. A possible solution to the problem was proposed based on a newly developed modified state surface approach. The discussions are limited for isotropic conditions. Copyright © 2015 John Wiley & Sons, Ltd.     

Generalized plasticity state parameter‐based model for saturated and unsaturated soils. Part II: Unsaturated soil modeling

The aim of this paper is to extend the generalized plasticity state parameter‐based model presented in part 1 to reproduce the hydro‐mechanical behavior of unsaturated soils. The proposed model is based on two pairs of stress–strain variables and a suitable hardening law taking into account the bonding—debonding effect of suction and degree of saturation. A generalized state parameter for unsaturated state is proposed to reproduce soil behavior using a single set of material parameters. Generalized plasticity gives a suitable framework to reproduce not only monotonic stress path but also cyclic behavior. The hydraulic hysteresis during a drying—wetting cycle and the void ratio effect on the hydraulic behavior is introduced. Comparison between model simulations and a series of experimental data available, both cohesive and granular, are given to illustrate the accuracy of the enhanced generalized plasticity equation. Copyright © 2010 John Wiley & Sons, Ltd.     

A bounding surface model for anisotropically overconsolidated clay incorporating thermodynamics admissible rotational hardening rule

A bounding surface model is formulated to simulate the behavior of clays that are subject to an anisotropic consolidation stress history. Conventional rotational hardening is revisited from the perspective of thermodynamics. As the free energy cannot be accumulated infinitely upon critical state failure, the deviatoric back stress must vanish. This requires the rotated yield surface to be turned back to eventually align on the hydrostatic axis in the stress plane. Noting that most of the previous propositions violate this restriction, an innovative rotational hardening rule is formulated that is thermodynamically admissible. The bounding surface framework that employs the modified yield surface is applied to simulate elastoplastic deformations for overconsolidated clays, with which the overprediction of strength on the “dry” side can be greatly improved with reasonable results. Other important features, including contractive or dilative response and hardening or softening behavior, can also be well-captured. It has been shown that the model can simulate three types of reconstituted clays that are sheared with initial conditions over a wide range of anisotropic consolidation stress ratios and overconsolidation ratios under both triaxial undrained and drained conditions. Limitations and potential improvement of the model regarding the fabric anisotropy at critical state have been discussed.     

A plasticity constitutive model for unsaturated,anisotropic, nonexpansive soils

The paper describes and evaluates an incremental plasticity constitutive model for unsaturated, anisotropic, nonexpansive soils (CMUA). It is based on the modified Cam-Clay (MCC) model for saturated soils and enhances it by introducing anisotropy (via rotation of the MCC yield surface) and an unsaturated compressibility framework describing a double dependence of compressibility on suction and on the degree of saturation of macroporosity. As the anisotropic and unsaturated features can be activated independently, the model is downwards compatible with the MCC model. The CMUA model can simulate effectively: the dependence of compressibility on the level of developed anisotropy, uniqueness of critical state independent of the initial anisotropy, an evolving compressibility during constant suction compression, and a maximum of collapse. The model uses Bishop's average skeleton stress as its first constitutive variable, favouring its numerical implementation in commercial numerical analysis codes (eg, finite element codes) and a unified treatment of saturated and unsaturated material states.     

PPP/SINS紧耦合系统仿真的研究与分析

在捷联惯导(SINS)和GPS卫星接收机进行紧耦合的研究中,采用差分定位进行紧耦合的方法比较成熟,而关于精密单点定位(PPP)与捷联惯导紧耦合的研究还比较少。本文对精密单点定位与捷联惯导紧组合系统进行了Matlab仿真,利用数学解析的方法产生机载运动轨迹,通过设置系统的参数,获得仿真SINS和GPS数据;然后,通过PPP/SINS紧组合系统的仿真程序解算,将定位结果与PPP的结果比较,表明PPP/SINS紧组合导航定位的结果比PPP的精度和可靠性好,而且收敛的速度更快,同时也验证了算法的正确性。最后,分析了不同等级惯导对定位精度的影响。