Semi-analytical solution for drained expansion analysis of a hollow cylinder of critical state soils

The expansion of a thick-walled hollow cylinder in soil is of non-self-similar nature that the stress/deformation paths are not the same for different soil material points.As a result,this problem cannot be solved by the common self-similar-based similarity techniques.This paper proposes a novel,exact solution for rigorous drained expansion analysis of a hollow cylinder of critical state soils.Considering stress-dependent elastic moduli of soils,new analytical stress and displacement solutions for the nonself-similar problem are developed taking the small strain assumption in the elastic zone.In the plastic zone,the cavity expansion response is formulated into a set of first-order partial differential equations(PDEs)with the combination use of Eulerian and Lagrangian descriptions,and a novel solution algorithm is developed to efficiently solve this complex boundary value problem.The solution is presented in a general form and thus can be useful for a wide range of soils.With the new solution,the non-self-similar nature induced by the finite outer boundary is clearly demonstrated and highlighted,which is found to be greatly different to the behaviour of cavity expansion in infinite soil mass.The present solution may serve as a benchmark for verifying the performance of advanced numerical techniques with critical state soil models and be used to capture the finite boundary effect for pressuremeter tests in small-sized calibration chambers.

Predicted Critical State Based on Invariance of the Lyapunov Exponent in Dual Spaces

Critical states in disordered systems,fascinating and subtle eigenstates,have attracted a lot of research interests.However,the nature of critical states is difficult to describe quantitatively,and in general,it cannot predict a system that hosts the critical state.We propose an explicit criterion whereby the Lyapunov exponent of the critical state should be 0 simultaneously in dual spaces,namely the Lyapunov exponent remains invariant under the Fourier transform.With this criterion,we can exactly predict a one-dimensional quasiperiodic model which is not of self-duality,but hosts a large number of critical states.Then,we perform numerical verification of the theoretical prediction and display the self-similarity of the critical state.Due to computational complexity,calculations are not performed for higher dimensional models.However,since the description of extended and localized states by the Lyapunov exponent is universal and dimensionless,utilizing the Lyapunov exponent of dual spaces to describe critical states should also be universal.Finally,we conjecture that some kind of connection exists between the invariance of the Lyapunov exponent and conformal invariance,which can promote the research of critical phenomena.

Determination of critical state line(CSL)for silty-sandy iron ore tailings subjected to low-high confining pressures

The disposal of filtered tailings in high dry stacks can induce particle breakage,changing the material's behaviour during the structure's lifetime.The grading changes influence material properties at the critical state,and this is not mature for intermediate artificial soils(tailings)in a broad range of confining pressures.In this paper,it aims to describe the behaviour of iron ore tailings in a spectrum of confining pressures broader than the reported in previous studies.A series of consolidated drained(CD)triaxial tests was carried out with confining pressures ranging from 0.075 MPa to 120 MPa.These results show that the amount of breakage plays an essential role in the response of iron ore tailings.The existence of curved critical state line(CSL)in both specific volume(ν)-logarithm of mean effective stress(p′)and deviatoric stress(q)-mean effective stress(p′)planes,and different responses in the deviatoric stress-axial strain-volumetric strain curves were verified.An inverse S-shaped equation was proposed to represent the silty-sandy tailings'behaviour up to high pressures onν-lnp′plane.The proposed equation provides a basis for enhancing constitutive models and considers the evolution of the grading up to severe loading conditions.The adjustment considered three regions with different responses associated with particle breakage at different pressure levels.

Electrical Tree Simulation Based on the Self-Organization Criticality

So far much effort has been made to understand the development of electrical treeing. For the simulation based study of electrical treeing, the most common method is to apply DBM stochastic model to simulate the growing of electrical treeing patterns. Previous simulation results showed that this stochastic model is capable of simulating the real electrical treeing patterns in a point-to-plane electrode system. However, this model only allows the tree channels to propagate on equipotential lines proportional to local electrical field. Therefore, it is necessary to develop a novel stochastic model to simulate the electrical patterns in order to get a good agreement with experimental results.

CALCULATIONS OF THE PHASE EQUILIBRIA AND CRITICAL CURVES WITH THE EQUATION OF STATE FOR BINARY MIXTURES

A rational equation of state of the perturbation type with a repulsion and attraction term has been applied to reproduce critical curves of six different binary systems up to high temperatures and pressures. A square well potential for intermolecular interaction is used. With pairwise combination rules for these potentials three adjustable parameters are needed. The experimental critical point and phase equilibrium data are compared with the values predicted using the equation of state. Good agreement is obtained for the analysis of the critical pressure composition data and molar volumes.

Effects of water content on the shear behavior and critical state of glacial till in Tianmo Gully of Tibet, China

Glacial tills are widely distributed in Tibet, China, and are highly susceptible to landslides under intense rainfalls. Failures of the slope during rainfall are closely related to the shear behavior of glacial tills at different moisture conditions. This study investigates the shear behavior and critical state of saturated and unsaturated glacial tills through a series of drained direct shear tests. The tests were conducted on two types of compacted glacial tills with different water contents and total normal stresses. A strain softening mode of failure is observed for all water content conditions accompanied by noticeable dilation. Dilatancy is found to decrease with increasing water content. Unsaturated samples showed increased rates of dilation as water content is decreased for all applied normal stresses a behavior which cannot be predicted well by classical stressdilatancy models. Furthermore, it was found that the Critical State Line(CSL), plotted on the(e-ln) plane, can be used to define the shear behavior of unsaturated glacial tills at different water contents.The CSL of saturated glacial tills run parallel to this line. The experimental results in this study are aimed to provide a basic understanding to the underlying failure mechanisms of glacial tills.

A critical state subloading surface model of sands with shear hardening

Based on the framework of critical state soil mechanics,a subloading surface plastic model for sand, being applicable to cyclic loading, was proposed. The model can be used to describe strain softening behaviour of sand under monotonic loading when the similarity-ratio equals to unity. The characteristics of the model are as follows: 1) A reverse bullet-shaped yield surface is adopted to ensure accurate prediction of the behavior of sand, instead of bullet-shaped or elliptical yield surface in Cam-Clay model. 2) No unique relationship between void ratio and the mean normal stress for sand prevents the direct coupling of yield surface size to void ratio, so incremental deviatoric strain hardening rule is used. 3) The model combines the concept of state-dependent dilatancy by incorporating state parameter in Rowe's stress dilatancy equation, which accounts for the dependence of dilatancy on the stress state and the material internal state. A single set of model constants, which is calibrated, can simulate stress-strain response under different initial void ratios and different confine pressures. The model is validated true by comparing predicted results with experimental results under monotonic and cyclic loading conditions.

A unified critical state model for geomaterials with an application to tunnelling

This paper is prepared in honour of Professor E.T.Brown for his outstanding contributions to rock mechanics and geotechnical engineering and also for his personal influence on the first author’s research career in geomechanics and geotechnical engineering.As a result,we have picked a topic that reflects two key research areas in which Professor E.T.Brown has made seminal contributions over a long and distinguished career.These two areas are concerned with the application of the critical state concept to modelling geomaterials and the analysis of underground excavation or tunnelling in geomaterials.Partially due to Professor Brown’s influence,the first author has also been conducting research in these two areas over many years.In particular,this paper aims to describe briefly the development of a unified critical state model for geomaterials together with an application to cavity contraction problems and tunnelling in soils.

Thermo-mechanical constitutive modeling of unsaturated clays based on the critical state concepts

A thermo-mechanical constitutive model for unsaturated clays is constructed based on the existingmodel for saturated clays originally proposed by the authors. The saturated clays model was formulatedin the framework of critical state soil mechanics and modified Cam-clay model. The existing model hasbeen generalized to simulate the experimentally observed behavior of unsaturated clays by introducingBishop＇s stress and suction as independent stress parameters and modifying the hardening rule and yieldcriterion to take into account the role of suction. Also, according to previous studies, an increase intemperature causes a reduction in specific volume. A reduction in suction （wetting） for a given confiningstress may induce an irreversible volumetric compression （collapse）. Thus an increase in suction （drying）raises a specific volume i.e. the movement of normal consolidation line （NCL） to higher values of voidratio. However, some experimental data confirm the assumption that this reduction is dependent on thestress level of soil element. A generalized approach considering the effect of stress level on themagnitude of clays thermal dependency in compression plane is proposed in this study. The number ofmodeling parameters is kept to a minimum, and they all have clear physical interpretations, to facilitatethe usefulness of model for practical applications. A step-by-step procedure used for parameter calibrationis also described. The model is finally evaluated using a comprehensive set of experimental datafor the thermo-mechanical behavior of unsaturated soils.2015 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

An approximate nonlinear modified Mohr-Coulomb shear strength criterion with critical state for intact rocks

In this paper, the Mohr-Coulomb shear strength criterion is modified by mobilising the cohesion and internal friction angle with normal stress, in order to capture the nonlinearity and critical state concept for intact rocks reported in the literature. The mathematical expression for the strength is the same as the classical form, but the terms of cohesion and internal friction angle depend on the normal stress now,leading to a nonlinear relationship between the strength and normal stress. It covers both the tension and compression regions with different expressions for cohesion and internal friction angle. The strengths from the two regions join continuously at the transition of zero normal stress. The part in the compression region approximately satisfies the conditions of critical state, where the maximum shear strength is reached. Due to the nonlinearity, the classical simple relationship between the parameters of cohesion, internal friction angle and uniaxial compressive strength from the linear Mohr-Coulomb criterion does not hold anymore. The equation for determining one of the three parameters in terms of the other two is supplied. This equation is nonlinear and thus a nonlinear equation solver is needed. For simplicity, the classical linear relationship is used as a local approximation. The approximate modified Mohr-Coulomb criterion has been implemented in a fracture mechanics based numerical code FRACOD,and an example case of deep tunnel failure is presented to demonstrate the difference between the original and modified Mohr-Coulomb criteria. It is shown that the nonlinear modified Mohr-Coulomb criterion predicts somewhat deeper and more intensive fracturing regions in the surrounding rock mass than the original linear Mohr-Coulomb criterion. A more comprehensive piecewise nonlinear shear strength criterion is also included in Appendix B for those readers who are interested. It covers the tensile, compressive, brittle-ductile behaviour transition and the critical state, and gives smooth transitions.

A circular zone counting method of identifying a Duffing oscillator state transition and determining the critical value in weak signal detection

Identifying state transition and determining the critical value of the Duffing oscillator are crucial to indicating external signal existence and have a great influence on detection accuracy in weak signal detection. A circular zone counting （CZC） method is proposed in this paper, by combining the Duffing oscillator＇s phase trajectory feature and numerical calculation for quickly and accurately identifying state transition and determining the critical value, to realize a high- efficiency weak signal detection. Detailed model analysis and method construction of the CZC method are introduced. Numerical experiments into the reliability of the proposed CZC method compared with the maximum Lyapunov exponent （MLE） method are carried out. The CZC method is demonstrated to have better detecting ability than the MLE method, and furthermore it is simpler and clearer in calculation to extend to engineering application.

Critical Spreading of Active Region in a Ladder Model Possessing Infinite AbsorbingStates

The spreading of active region of the ladder model is simulated. Finite-time scaling behaviors are observedin the vicinity of the critical point.

Ground states for asymptotically periodic quasilinear Schrdinger equations with critical growth

For a class of asymptotically periodic quasilinear Schr？dinger equations with critical growth the existence of ground states is proved.First applying a change of variables the quasilinear Schr？dinger equations are reduced to semilinear Schr？dinger equations in which the corresponding functional is well defined in H1 RN .Moreover there is a one-to-one correspondence between ground states of the semilinear Schr？dinger equations and the quasilinear Schr？dinger equations.Then the mountain-pass theorem is used to find nontrivial solutions for the semilinear Schr？dinger equations. Finally under certain monotonicity conditions using the Nehari manifold method and the concentration compactness principle the nontrivial solutions are found to be exactly the same as the ground states of the semilinear Schr？dinger equations.

Critical State Sedimentation Line of Soft Marine Clays

The compression behavior responsible for unity sensitivity is very valuable in quantitative assessment of the effects of soil structure on the compression behavior of soft marine sediments. However, the quantitative assessment of such effects is not possible because of unavailability of the formula for the compression curve of marine sediments responsible for unit sensitivity. In this study, the relationship between the remolded state and the conventional critical state line is presented in the deviator stress versus mean effective stress plot. The analysis indicates that the remolded state is on the conventional critical state line obtained at a relatively small strain. Thus, a unique critical state sedimentation line for marine sediments of unit sensitivity is proposed. The comparison between the critical state sedimentation line proposed in this study and the existing normalized consolidation curves obtained from conventional oedometer tests on remolded soils or reconstituted soils explains well the

Quantitative determination of the critical points of Mott metal–insulator transition in strongly correlated systems

Mottness is at the heart of the essential physics in a strongly correlated system as many novel quantum phenomena occur in the metallic phase near the Mott metal–insulator transition. We investigate the Mott transition in a Hubbard model by using the dynamical mean-field theory and introduce the local quantum state fidelity to depict the Mott metal–insulator transition. The local quantum state fidelity provides a convenient approach to determining the critical point of the Mott transition. Additionally, it presents a consistent description of the two distinct forms of the Mott transition points.

Self-organized Criticality Model for Ocean Internal Waves

In this paper, we present a simple spring-block model for ocean internal waves based on the self-organized criticality （SOC）. The oscillations of the water blocks in the model display power-law behavior with an exponent of -2 in the frequency domain, which is similar to the current and sea water temperature spectra in the actual ocean and the universal Garrett and Munk deep ocean internal wave model [Geophysical Fluid Dynamics 2 （1972） 225; J. Geophys. Res. 80 （1975） 291]. The influence of the ratio of the driving force to the spring coefficient to SOC behaviors in the model is also discussed.

Self-Organized Criticality Analysis of Earthquake Model Based on Heterogeneous Networks

The original Olami-Feder-Christensen （OFC） model, which displays a robust power-law behavior, is a quasistatic two-dimensional version of the Burridge-Knopoff spring-block model of earthquakes. In this paper, we introduce a modified OFC model based on heterogeneous network, improving the redistribution rule of the original model. It can be seen as a generalization of the originM OFC model We numerically investigate the influence of the parameters θandβ, which respectively control the intensity of the evolutive mechanism of the topological growth and the inner selection dynamics in our networks, and find that there are two distinct phases in the parameter space （θ,β）. Meanwhile, we study the influence of the control parameter a either. Increasing a, the earthquake behavior of the model transfers from local to global.

A Modified Earthquake Model of Self-Organized Criticality on Small World Networks

A modified Olami Feder-Christensen model of self-organized criticality on a square lattice with the properties of small world networks has been studied.We find that our model displays power-law behavior and the exponent τ of the model depends on φ,the density of long-range connections in our network.

Influence of Selective Edge Removal and Refractory Period in a Self-Organized Critical Neuron Model

A simple model for a set of integrate-and-fire neurons based on the weighted network is introduced. By considering the neurobiological phenomenon in brain development and the difference of the synaptic strength, we construct weighted networks develop with link additions and followed by selective edge removal. The network exhibits the small-world and scale-free properties with high network efficiency. The model displays an avalanche activity on a power-law distribution. We investigate the effect of selective edge removal and the neuron refractory period on the self-organized criticality of the system.

The Character of Shear-wave Splitting in Marble in the Critical State of Rupture

This paper mainly observed and analyzed the character of shear-wave splitting in rock specimens while they were in the critical state of rupture. The rock specimens for study are made of Laizhou marble from Shandong, China. A series of records were obtained from two rock specimens when they were in the critical state of rupture. The result shows that, in the critical state just before rock rupture, there may be the phenomenon of rise and fall in the time delay of shear-wave splitting, even though the load was kept constant. That is to say, the time delay of shear-wave splitting may have a falling process before rock rupture.