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.

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.

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

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.

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.

Numerical analysis of slope collapse using SPH and the SIMSAND critical state model

Geological disasters such as slope failure and landslides can cause loss of life and property.Therefore,reproducing their evolution process is of great importance for risk assessment and mitigation.The recently developed SIMSAND critical state sand model combined with the smoothed particle hydrodynamics(SPH)method is adopted in this work to study slope failure under large deformations.To illustrate the efficiency and accuracy of the SIMSAND-SPH approach,a series of slope collapse studies using the discrete element method(DEM)considering various particle shapes(i.e.spherical,tetrahedral and elongated)is adopted as benchmarks.The parameters of the SIMSAND model are calibrated using DEM triaxial tests.In comparison to the DEM simulations,the runout distance and final slope height are well characterized with the SIMSAND-SPH approach with less computational cost.All comparisons show that the SIMSAND-SPH approach is highly efficient and accurate,which can be an alternative numerical tool to simulate real scale granular flow.

Cyclic liquefaction screening of sand with non-plastic fines:Critical state approach

There have been significant advances in the application of critical state,CS,in liquefaction potential assessment.This was done by comparing state parameter,j with estimated characteristic cyclic stress ratio,CSR due to an earthquake.A cyclic resistance ratio,CRR curve,which can be determined from cyclic liquefaction tests,separates historical liquefied and non-liquefied data points(j,CSR).On the other hand,the concepts of equivalent granular state parameter,j*,which was developed for sands with fines,can be used in lieu j to provide a unifying framework for characterizing the undrained response of sands with non/low plasticity fines,irrespective of fines content(fc).The present work combines these two propositions,and by merely substituting j*for j into the aforementioned CS approach to capture the influence of fc.A series of static and cyclic triaxial tests were conducted,separately and independently of the concept of j*,for sand with up to fc of 30%.The clean sand was collected from Sabarmati river belt at Ahmedabad city in India which was severely affected during the Bhuj earthquake,2001.The experimental data gave a single relation for CRR and j*which was then used to assess liquefaction potential for a SPT based case study,where fc varies along the depth.The prediction matched with the field observation.

Effect of fiber-reinforcement on the mechanical behavior of sand approaching the critical state

Several types of ground improvement methods that employ fiber-reinforcement have been developed in recent years.A series of consolidated drained triaxial compression tests has been conducted here to examine the effect of short fibers on the mechanical properties of Toyoura sand.Sand with 0%,0.2%,0.4%,and 1%fiber contents,prepared to yield random distribution,was sheared under several confining pressures and controlled via their initial relative densities.The test results showed that the maximum and residual deviatoric stresses increased,whereas the volumetric expansion decreased with an increase in fiber content.Although the stress ratio h(=q/p′)and specific volume changed depending on the fiber content and confining pressure with shear progression,they each reached the same values for a definite fiber content at the end of shearing,independent of initial relative density.In other words,the unique critical state line can be found for a definite fiber content.Moreover,the greater the fiber content,the larger the slope of the critical state line at the end of shearing.Additionally,as the length of fibers shortened with the same percentage of fiber inclusions in sand,the deviatoric stress and the stress ratio decreased,approaching the shear-strain-volumetric response of unreinforced sand.

Modeling for critical state line of granular soil with evolution of grain size distribution due to particle breakage

Determination of the critical state line(CSL)is important to characterize engineering properties of granular soils.Grain size distribution(GSD)has a significant influence on the location of CSL.The influence of particle breakage on the CSL is mainly attributed to the change in GSD due to particle breakage.However,GSD has not been properly considered in modeling the CSL with influence of particle breakage.This study aims to propose a quantitative model to determine the CSL considering the effect of GSD.We hypothesize that the change of critical state void ratio with respect to GSD is caused by the same mechanism that influences of the change of minimum void ratio with respect to GSD.Consequently,the particle packing model for minimum void ratio proposed by Chang et al.(2017)is extended to predict critical state void ratio.The developed model is validated by experimental results of CSLs for several types of granular materials.Then the evolution of GSD due to particle breakage is incorporated into the model.The model is further evaluated using the experimental results on rockfill material,which illustrates the applicability of the model in predicting CSL for granular material with particle breakage.

DEM investigation of strength and critical state behaviours of granular materials under true triaxial loadings

This paper investigates the strength and critical state(CS)behaviours of granular materials via DEM simulations of true triaxial drained tests under three different loading modes including constant b(in-termediate stress ratio)tests with constantσ'1(major principal stress),constant p(mean pressure)and constantσ'3(minor principal stress)respectively.To this end,a series of samples are generated with the same particle size distribution,and with the confining stresses ranging from 100 kPa to 900 kPa.The CS is achieved for all samples.Both the macroscopic behaviours and the microscopic behaviours are examined and compared considering different loading modes,confining stresses and intermediate stress ratios(b).The critical state lines(CSLs)are found to be unique and independent of the loading modes,but dependent on the b values.The CSLs with b=0 and b=1 form the two boundaries of CSLs respectively beyond which CSLs under all other b tests cannot go beyond.Six different strength criteria are examined and compared in terms of both peak and CS failures.The Mohr-Coulomb strength criterion is found to be only suitable for axisymmetric loading conditions.The Lade-Duncan criterion is only suitable for describing peak strengths,which is dependent on the loading modes and confining stresses.The Satake criterion and Matsuoka-Nakai criterion are the more appropriate strength criteria for describing CS failures,indicating that the CS values of both the Satake parameter and the Matsuoka-Nakai parameter describe an inherent property that characterizes the CS failure for a given type of soil.The CS mechanical coordination number is fitted by a curved line for a given b value,which is unique regardless of the loading modes.The peak and CS values of both major and minor principal fabric tensors decrease with increasing b values,while they increase with increasing b values for the intermediate principal fabric tensor.

Critical state-induced emergence of superior magnetic performances in an iron-based amorphous soft magnetic composite

Soft magnetic composites(SMCs)play a pivotal role in the development of high-frequency,miniaturization and complex forming of modern electronics.However,they usually suffer from a trade-off between high magnetization and good magnetic softness(high permeability and low core loss).In this work,utilizing the order modulation strategy,a critical state in a FeSiBCCr amorphous soft magnetic composite(ASMC),consisting of massive crystal-like orders(CLOs,∼1 nm in size)with the feature ofα-Fe,is designed.This critical-state structure endows the amorphous powder with the enhanced ferromagnetic exchange interactions and the optimized magnetic domains with uniform orientation and fewer micro-vortex dots.Superior comprehensive soft magnetic properties at high frequency emerge in the ASMC,such as a high saturation magnetization(Ms)of 170 emu g^(-1)and effective permeability(µ_(e))of 65 combined with a core loss(Pcv)as low as 70 mW cm^(-3)(0.01 T,1 MHz).This study provides a new strategy for the development of high-frequency ASMCs,possessing suitable comprehensive soft magnetic performance to match the requirements of the modern magnetic devices used in the third-generation semiconductors and new energy fields.

DEM simulations of critical state behaviour of granular materials under various drained triaxial stress path tests

The present study investigates the critical state behaviour of granular assemblies composed of clumped particles under four different drained axisymmetric triaxial stress paths,using the discrete element method(DEM).A series of numerical samples were prepared at initial states with different density indexes(1D)and different initial confining pressures(ρ′0).These samples were sheared to large strains,at which constant stresses and volumes were maintained to reach the critical state.The evolution of stress ratio under the same loading mode(for the same intermediate principal stress ratio,b)is shown to yield an almost identical behaviour independent of stress paths,whereas the stress-strain response depends on the stress paths.Four different axisymmetric stress paths all share the same unique friction angle at critical state,indicating the Mohr-Coulomb failure criterion is the appropriate critical state strength criterion,which is at least true for the axisymmetric stress conditions.A unique coordination number(CN)is achieved at the critical state for a given po,which is independent of the stress path.The critical state CN is found to increase with the increase in po,which could be attributed to the decrease in the critical state void ratio(ec)as mean effective stress(ρ′0)increases.Interestingly,a unique linear functional relationship is found between the critical state values of cN and ec,and a unique polynomial functional relationship is found between the critical state values of CN andρ′.These functional relationships indicate no dependency on the stress paths or loading modes,thus characterizing unique features at critical states at both macroscopic and microscopic levels for a given type of granular material.

Critical state shear behavior of the soil-structure interface determined by discrete element modeling

The interface between soil and structure can be referred to as a soil-structure system, and its behavior plays an important role in many geotechnical engineering practices, In this study, results are presented from a series of monotonic direct shear tests performed on a sand-structure interface under constant normal stiffness using the discrete element method （DEM）. Strain localization and dilatancy behavior of the interface is carefully examined at both macroscopic and microscopic scales. The effects of soil initial relative density and normal stress on the interface shear behavior are also investigated, The results show that a shear band progressively develops along the structural surface as shear displacement increases. At large shear displacement a unique relationship between stress ratio and void ratio is reached in the shear band for a certain normal stress, indicating that a critical state exists in the shear band. It is also found that the thickness and void ratio of the shear band at the critical state decreases with increasing normal stress. Comparison of the DEM simulation results with experimental results provides insight into the shear behavior of a sand-structure interface and offers a means for quantitative modeling of such interfaces based on the critical state soil mechanics.

Discrete element modelling of strength and critical state characteristics of granular materials under axial compression and axial extension stress path tests

The critical state soil mechanics(CSSM)framework has been widely used across a range of problems in geomechanics involving complex loading conditions.However,the uniqueness of the critical state has been disputed for many years and it remains a controversial issue.Motivated by previous investigations,a series of discrete element method(DEM)simulations were performed under both axial compression(AC)and axial extension(AE)stress paths.All samples were isotropically compressed at varying mean normal effective stresses(confining pressures)and sheared to a large axial strain of approximately 60%.It is found that there exist unique values of critical void ratios and stress ratios under critical state,which are independent of the samples’initial packings but dependent on stress paths.And the critical strength(stress ratio)for the AC stress path tests is higher than that for the AE stress path.The critical state lines(CSLs)are found to path-dependent but unique for each stress path.A unique linear relationship between the critical coordination numbers and critical void ratios is identified under the AC and AE stress paths respectively,but such a relationship depends on the stress paths.It is also found that there exist unique values of microscopic parameters in terms of deviator fabric under critical state,which are independent of the samples’initial packings but dependent on stress paths.All these simulation results lead to the conclusion of non-uniqueness of CSLs from both macroscopic and microscopic viewpoints.

Numerical analysis of column collapse by smoothed particle hydrodynamics with an advanced critical state-based model

The complex behavior of granular material considering large deformation and post-failure is of great interest in the geotechnical field.Numerical prediction of these phenomena could provide useful insights for engineering design and practice.In this paper,we propose a novel numerical approach to study soil collapse involving large deformation.The approach combines a recently developed critical state-based sand model SIMSAND for describing complex sand mechanical behaviors,and the smoothed particle hydrodynamics(SPH)method for dealing with large deformation.To show the high efficiency and accuracy of the proposed approach,a series of column collapses using discrete element method(DEM)and considering the influence of particle shapes(i.e.spherical shape(SS),tetrahedral shape(TS),and elongated shape(ES))were adopted as benchmarks and simulated by the proposed method.The parameters of SIMSAND were calibrated from the results of DEM triaxial tests on the same samples.Compared with the results of DEM simulations and reference solutions derived by published collapse experiments,the runout distance and final height of specimens with different particle shapes simulated by SPH-SIMSAND were well characterized and incurred a lower computational cost.Comparisons showed that the novel SPH-SIMSAND approach is highly efficient and accurate for simulating collapse,and can be a useful numerical analytical tool for real scale engineering problems.

Kinetics of Hydrothermal Reactions of Minerals in Near-critical and Supercritical Water

This work presents new experimental results on the kinetics of mineral dissolution in near-critical and supercritical water in a temperature range (T) from 25 to 400°C and a constant pressure of 23 MPa. Kinetic experiments were carried out by using a flow reactor (packed bed reactor) of an open system. The dissolution rates of albite and magnetite were measured under these experimental conditions. Na, Al and Si release rates for albite dissolution in water were measured as a function of the temperature and flow velocity in the reaction system. The maximum release rates of Na, Al and Si of albite dissolution in the hydrothermal flow systems under different flow velocities were always obtained at 300°C, that is to say, the maximum albite dissolution rates in the flow systems, regardless of different flow rates, were repeatedly measured at 300°C. Results indicate a wide fluctuation in albite dissolution rates occurring close to the critical point of water. The dissolution rates increased when the temperatures increased from 25 to 300°C and decreased when the temperatures increase from 300 to 400°C. At some flow velocities, the dissolution rates rose as the temperature surpassed 374°C. Albite dissolution was incongruent in water at most temperatures. It was only at 300°C that albite dissolution was congruent. The albite dissolution from 25 to 300°C (at 23 MPa) will change from incongruent to congruent, whereas from subcritical 300 to 400°C (at 23 MPa), the dissolution will change from congruent to incongruent. The release ratio of Al/Si (or Na/Si) is positive at T<300°C, and it is negative at T>300°C. The dissolution rates of magnetite in water increased with increasing T until T at the critical point of water or around it. The authors believe that this is caused by the wide fluctuations in water properties under the conditions from the near-critical to supercritical state.

A Study of Near-and Super-Critical Fluids Using Diamond Anvil Cell and in-Situ FT-IR Spectroscopy

The phase relation and solution structure of water and NaCl aqueous solution have been observed and examined by using the hydrothermal diamond anvil cell (HDAC) at elevated temperatures and pressures and the in situ FT-IR spectroscopy. The temperature of observations ranges from 25 to 850°C and the pressure up to 10 or 30 kb. At first, we observed the phase transition process from halite+liquid+vapour (H+L+V) to L+H, then to L (or supercritical fluid, SCF), and another path: H+L+V→L+V→L (or SCF) in heating process. By means of the visual microscope, the authors found that in the L+V immiscibility field L+V exhibits an ordered structure, i.e. a large visual cluster of solvent around ions. The liquid phase is manifested by vapour bubbles. When phase transitions are observed, the authors examined their infrared spectra by using the FT-IR microscopy simultaneously. In the case of the phase transition from liquid (L) to liquid + vapor (L+V) immisciblity field of NaCl solutions, a sudden change (strong frequency shift) of infrared spectra of the aqueous solution is observed near the critical temperature of water as the temperature is raised from 25 to 650°C. The frequency of the maximum intensity of OH symmetric and asymmetric vibration varies with respect to temperature. The sharp peak of the OH stretching vibration of the maximum intensity appears in an interval from 300 to 400°C. It is indicated that the hydrogen bonding network is weakened and broken at last near the critical point of water, which causes the aqueous solution to become more associated. Besides, a pressure indicator (a mineral or compound) was introduced to the HDAC.

Mechanical behavior of iron ore tailings under standard compression and extension triaxial stress paths

The disposal of mining tailings has increasingly focused on the use of dry stacks.These structures offer more security since they use filtered and compacted material.Because of the construction method and the heights achieved,the material that compounds the structure can be subjected to different stress paths along the failure plane.The theoretical framework considered in the design of these structures generally is the critical state soil mechanics(CSSM).However,the data in the literature concerning the uniqueness of critical state line(CSL)is still controversial as the soil is subjected to different stress paths.With respect to tailings,this question is even more restricted.This paper studies two tailings with different gradings due to the beneficial processes over extension and compression paths.A series of drained and undrained triaxial tests was conducted over a range of initial densities and stress levels.In the q-p'plane,different critical stress ratio(M)values were obtained for compression and extension stress paths.However,the critical state friction angle is very similar with a slightly higher critical state friction angle for extension tests.Curved stress path dependent CSLs were obtained in the n-lnp0 plane with the extension tests below the CSL defined in compression.Regarding the fines content,the studied tailings presented very similar M and critical state friction angle values.However,the fines content af-fects the volumetric behavior of the studied tailings and the CSLs on the n-lnp0 plane shift downwards with the increasing fines content for compression and extension tests.In relation to dilatancy analysis,the fines content did not present an evident influence on the dilatancy of the materials.However,different values of mean stress ratio N were obtained between compression and extension tests and can corroborate the existence of non-unique CSLs for these materials.

Multistage Triaxial Behavior of Shallow Landslide Hazard Site Soil of Rangamati Sadar Area, Bangladesh

The soil samples were collected from a shallow landslide hazard site of the Rangamati Sadar in Bangladesh to determine the shear strength properties of the soil. Multistage triaxial consolidation undrained test has become worldwide more accepted to determine the shear strength parameters. Multistage triaxial undrained tests were performed on five samples taken from five different depths of boreholes. Samples were evaluated under two natural conditions and three remolded situations. Samples were consolidated before shearing at confining pressures from 50 kPa to 1200 kPa. All the test results are discussed in terms of deviator stress versus axial strain, mean effective stress versus deviator curves, stress ratio versus axial strain, and excess p. w. p. versus axial strain curves. The samples consolidated at low effective stress first displayed peak positive values of excess p. w. p., followed by increased strains due to sample bulging failure, and only a few samples formed a shear surface failure. The strength parameters were estimated using the maximum deviator stress as the failure criterion i.e. the overall value of the cohesion is 20 kPa and the friction angle is 34°. Hence, the critical state line has been constructed and the critical state parameters have been calculated. The critical state stress ratio M was calculated to be 0.036. The shear strength of soil is one of the significant mechanical properties that are thoroughly used to assess the landslide and liquefaction potentiality of the soil.

Remolded Undrained Strength of Soils

Extensive data of undrained shear strength for various remolded soils are compiled to normalize the remolded undrained strength. Remolded soils have a wide spectrum of liquid limits ranging from 25% to 412%. It is found that the remolded undrained strength is a function of water content and liquid limit. Furthermore, a simple index designated as normalized water content w * is introduced for normalizing remolded undrained strength for various soils. The normalized water content w * is the ratio of water content to liquid limit. The relationship between the remolded undrained strength and the normalized water content can be expressed by a simple equation. The new simple equation is not only valuable theoretically for helping in assessing the in situ mechanical behavior, but also useful to ocean engineering practice.