Critical State Parameters Research Articles

Effect of the particle shape on the shear mechanical behavior of coral sand

Abstract Coral sand particles exhibit a wide range of shapes, which can be divided into four shapes, e.g., blocky, dendritic and rodlike, flaky, and shell debris. The particle shape of these mixtures is defined by the sphericity, concavity, aspect ratio, flatness and overall regularity, which ranges from 0 to 1. The effect of particle shape on the strength, crushing characteristics, and critical state parameter is systematically investigated through a series of triaxial drainage shear tests under different confining pressures. And the relationship between critical state parameters and mechanical parameters is established. The test results demonstrate the existence of an evident strain-hardening phenomenon in the stress–strain curve of coral sand, accompanied by a strain-softening phenomenon when the bias stress reaches its peak value. The sample is initially subjected to shear shrinkage, followed by shear expansion. The volumetric deformation of the coral sand decreased with increasing peripheral pressure. The particles are transformed from rough irregular shapes to smooth spheres as evidenced by an increase in the shape parameter. The greater the degree of irregularity in the shape of the particles, the more pronounced the resulting change in size reduction. In addition, the critical state parameter was found to be influenced by the shape of the coral sand particles and the mode of particle accumulation. The overall shear resistance of coral sand particles was found to depend on particle rearrangement in addition to particle surface roughness and interparticle friction. It is proposed that the general regularity critical state parameter equation relates the particle shape of coral sand to its critical state mechanical properties, which is of great importance to the practical application and research of coral sand in engineering, and provides an effective means of predicting mechanical properties granular materials.

Research on the State-Dependent Hyperbolic Model of the Interface between Spoil Mixture and Concrete

Abstract A series of large-scale direct shear tests were carried out to study the stress-strain relationship of the interface between the spoil mixture and concrete under different roughness conditions. The results showed that roughness significantly affects the shear strength properties and dilatancy characteristics of the interface. Under different roughness conditions, the shear stress ratio and the normal deformation of the interface tend to be stable after larger shear strain, and the interface presents the characteristics of a critical state. With the increase of shear strain, the void ratio of the interface shows the law of transformation from the initial void ratio to a certain stable void ratio. Based on the void ratio prediction formula of the interface, the relationship between roughness and critical state parameters was established, and the interface state parameters were introduced into the hyperbolic model. Finally, a state-dependent hyperbolic model of the interface considering the roughness was established. Importantly, the model can well reflect the shear stress-strain relationship of the interface under different roughness conditions.

Exploring the micro-to-macro response of granular soils with real particle shapes by way of μCT-aided DEM analyses

This contribution provides high-fidelity images of real granular materials with the aid of X-ray micro-computed tomography (μCT), and employs a multi-sphere representation to reconstruct non-spherical particles. Through discrete-element method (DEM) simulations of granular samples composed of these non-spherical clumps, the effect of particle shape on the macroscopic mechanical response and microscopic soil fabric evolution is examined for soil assemblies under triaxial compression. Simulation results indicate that materials with more irregular particles tend to show higher shear resistance in both peak and critical states, while exhibiting higher void ratio under isotropic loading conditions and in the critical state. The proposed critical state parameters for describing the sensitivity of the mean coordination number to confining pressures are larger as particles become more irregular. At a microscopic level of observation, directional and scalar parameters of particle contacts are sensitive to predefined particle shapes. More irregular materials appear to exhibit higher fabric anisotropy with respect to particle orientation in the critical state, while the branch vector is affected by both contact modes and particle shape. The critical stress ratio from the simulation results is validated by comparing with experimental results, and further found to be linearly linked to the shape-weighted fabric anisotropy indices.

Exploring Tailings Dam Stability Considering Uncertainties in the Critical State Parameters of the NorSand Model

Exploring Tailings Dam Stability Considering Uncertainties in the Critical State Parameters of the NorSand Model

Stability of Cauchy horizon in charged black holes surrounded by quintessential dark energy

By investigating the Quasinormal Modes of a massless neutral scalar field, we have explored the influence of dark energy on the strong cosmic censorship (SCC) of charged de Sitter-like black holes. The results indicate that SCC can consistently be violated as long as the black hole approaches extremality. However, as the state parameter σ=3ωf+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma = 3\\omega _f + 1$$\\end{document} of the dark energy increases and approaches zero, the width of SCC violation interval demonstrates an overall decreasing trend, converging towards zero. Specifically, our research has identified a critical state parameter σcrt\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _{\ ext {crt}}$$\\end{document} for dark matter. Beyond this critical value, enhancing the state parameter effectively mitigates SCC violations. However, at this critical threshold, the width of the violation interval stabilizes or marginally increase. These findings reveal a nuanced relationship between the asymptotic properties of black holes and the validity of the SCC, offering profound insights into potential mechanisms governing both the occurrence and alleviation of SCC violations.

X-ray CT quantification of in-situ fabric evolution and shearing behaviour of granular soils of different particle shapes

The role of particle shape on soil mechanical response has been studied extensively especially through numerical means. The underlying micro-mechanics of how particle shape may affect the soil mechanical responses at element scale remains unclear. Systematic micro-mechanical experiments that consider in-situ tracking of the evolution of fabric during the shearing process is missing. Aided by a miniaturised triaxial apparatus and X-ray computed tomography, this study presents a series of triaxial compression on four granular soils with different particle shapes yet the same mineralogy, grading and initial density. Evolution of three-dimensional soil fabric quantifiers during shearing was captured based on 192 full-field CT images. The results revealed that the initial shearing reduced the packing density without changing the particle packing pattern, followed by particle sliding and particle rotation which redistributed the force chains and formed a new packing pattern to resist shearing, causing strain localisation and reductions in both the contact number and concentration of contacts di-rection. Fabric anisotropy increased before reaching the peak and attained the maximum value as the soil approached the critical state. Particle shape, especially when quantified by overall regularity, or other combinations of descriptors, displayed more significant linear cor-relations with critical-state parameters than by local descriptor.

A new procedure for characterizing the critical intergranular contact state of non-plastic sand – fines mixed materials

A key and urgent scientific issue is how to characterize the complex intergranular contact state and mechanical behavior evolution of sand–fines mixed materials and then show how this state contributes to the static and dynamic properties of such materials. Both theoretical analyses and experimental data suggest that the mixes have different intergranular contact states as the fines content (FC) increases, and the mixed materials can be classified as sand-like, in-transition, or fines-like. The capability of the Rahman semi-empirical formula to predict the threshold fines content FCth—which distinguishes the regime of “fines in sand” (sand-dominated behavior) from that of “sand in fines” (fines-dominated behavior)—is verified using the basic material and mechanical properties of mixed materials from the literature. Developed from the method for determining the theoretical minimum void ratio, a new method that allows unified characterization of the critical intergranular contact state parameters FCin-min and FCin-max for in-transition soils is established based on the binary packing model, and FCin-min and FCin-max can be determined simply through explicit expressions that use some material physical indices of pure-sand and pure-fines materials. The proposed procedure offers significant advantages for evaluating the critical intergranular contact state and mechanical properties of sand–fines mixed materials in geotechnical engineering practice.

Intelligent Prediction of Critical State Parameters for Non-plastic Tailings and Soils Using Evolutionary Algorithms

Intelligent Prediction of Critical State Parameters for Non-plastic Tailings and Soils Using Evolutionary Algorithms

Multi-Segment State of Health Estimation of Lithium-ion Batteries Considering Short Partial Charging

State of health (SOH) is a critical state parameter of lithium-ion batteries (LIBs). Health indicators (HIs), which are derived from the measured features of LIBs, are used in the current data-driven SOH estimation techniques to determine SOH. However, the common partial charging and discharging make it challenging to derive reliable HIs. In this paper, a SOH estimation approach considering short partial charging is proposed. Unlike other techniques, the constant current charging stage is divided into short segments, the HI, based on the charging capacity and actual initial charging voltage, is extracted within each short segment, and a kernel ridge regression-based estimator is created to characterize the SOH mapping relationship. Subsequently, an estimator fusion frame is established to merge the estimates of the eligible segments, which is decided based on the actual start and end charging voltages of the partial charging. The effectiveness of the proposed approach is validated with two well-known LIBs aging datasets containing real partial charging cycles. The results are satisfactory in terms of accuracy, robustness to partial charging, and good generality to different types of LIBs. Effective SOH value can be deduced whenever the charging voltage range covers at least one short estimation segment.

Characterization and environmental sustainability of open pit coal mine overburden waste rock as pavement geomaterial

As the global economy grows and living standards increase, the use of gravel and sand is expected to nearly quadruple by 2060, putting twice as much strain on the environment as it does now. Local solutions to the global problem are always more sustainable and resilient. In recent times, coal mine overburden (OB) is an unprocessed, highly heterogenous waste of coal mining industries. However, it has proved to be a sound potential alterative of natural aggregate. The associated engineering properties are very site specific and are highly influenced by geology and exposed climate. A comprehensive laboratory testing program oriented at determining the geotechnical and geoenvironmental properties is implemented to investigate the suitability of the OB as pavement material. The load-deformation performance as pavement material is evaluated using 3D finite element modelling and environmental sustainability is assessed through streamlined Life cycle assessment (LCA). This inert geomaterial is acceptable as a pavement material for base and subbase layers with impact value of 28 %, and abrasion value 34 %. The California bearing ratio (CBR) of 76 at unsoaked and 61 at soaked conditions also affirm its choice as an excellent subgrade material. The critical state parameters of the fine aggregate defined the long-term serviceability as a subgrade material. The load-deformation behavior of overburden was found to be similar to the natural aggregate as a pavement material with comparable maximum deflection of 1.20 mm for OB and 1.25 mm for natural aggregate. The LCA revealed that OB are more environmentally sustainable than natural aggregates as base and subbase material. The study highlights the importance of proper characterization and testing of OB to ensure its safe and effective use in construction applications, providing robust local solutions to global problems.

Static Liquefaction Assessment Combining Shear Wave Velocity, Peak Strength and Soil Grading

A large set of undrained compression triaxial tests was carried out on different types of cohesionless soils, from sands to silty sands and silts. Shear wave velocity measurements were also carried out. These tests exhibit distinct state transitions ranging from flow liquefaction to strain softening or strain hardening. With the purpose of defining a framework to assess soil liquefaction, it was found that the ratio between the shear wave velocity (VS0) and the peak undrained deviatoric stress (qpeak), VS0/qpeak, could be accurately used to define a boundary between liquefaction and strain hardening for sands and between strain softening and strain hardening for silty sands and silts. Since this ratio is a function of the tested material, the prediction of these boundaries can be made as a function of soil grading, namely via the coefficient of uniformity, CU. Despite not being regarded as a strong geomechanical parameter, CU is easily determined from a grain-size distribution test and has an empirically proven correlation with critical state parameters.

Micro-mechanical insights into the stress transmission in strongly aggregating colloidal gel.

Predicting the mechanical response of soft gel materials under external deformation is of paramount importance in many areas, such as foods, pharmaceuticals, solid-liquid separations, cosmetics, aerogels, and drug delivery. Most of the understanding of the elasticity of gel materials is based on the concept of fractal scaling with very few microscopic insights. Previous experimental observations strongly suggest that the gel material loses the fractal correlations upon deformation and the range of packing fraction up to which the fractal scaling can be applied is very limited. In addition, correctly implementing the fractal modeling requires identifying the elastic backbone, which is a formidable task. So far, there is no clear understanding of the gel's elasticity at high packing fractions or the correct length scale that governs its mechanical response. In this work, we undertake extensive numerical simulations to elucidate the different aspects of stress transmission in gel materials. We observe the existence of two percolating networks of compressive and tensile normal forces close to the gel point. We also find that the probability distribution for the compressive and tensile parts normalized by their respective mean shows a universal behavior irrespective of various values of interaction potential and thermal energy and different particle size distributions. Interestingly, there are also a large number of contacts with zero normal force, and, consequently, a peak in the normal force distribution is observed at fn ≈ 0 even at higher pressures. We also identify the critical internal state parameters, such as the mean normal force, force anisotropies, and the average coordination number, and propose simple constitutive relations that relate different components of stress to internal state parameters. The agreement between our model prediction and the simulation observation is excellent. It is shown that the anisotropy in the force networks gives rise to the normal stress difference in soft gel materials. Our results strongly demonstrate that the mechanical response of the gel system is governed mainly by the particle length scale phenomena, with a complex interplay between the compressive and tensile forces at the particle contact.

A unified critical state parameter model for sand and overconsolidated clay in the framework of subloading surface theory

This paper presents a unified critical state parameter model for evaluating sand and overconsolidated clay, which is named as CASM-S. The model is formulated in terms of the modification of the clay and sand model, i.e., CASM, by incorporating the subloading surface theory with an overconsolidation state parameter R. Although the standard CASM proves to be useful in modelling overconsolidated clay and sand, the model (1) requires the rate of overconsolidated ratio to be constant which is in contrast to the observed behaviour of soils and (2) only allows elastic deformation to develop at the overconsolidated state that may underestimate the deformation corresponding to the peak stress or be unable to predict the actual stress path. By introducing a new material parameter u to those material properties of the standard CASM, the rate relationship of stress–strain for the CASM-S model is developed. The standard CASM can be either recovered or approximated as a special case of the overconsolidation state assumed in the CASM-S. The numerical integration of the newly proposed model is performed by the modified forward Euler method. Validation with undrained and drained overconsolidated clay and sand have demonstrated the capability of the CASM-S model to well predict the observed soil behaviours.

DEM-based study on the mechanical behaviors of sand-rubber mixture in critical state

This paper presents a numerical method to investigate the critical-state behaviors of the soft-rigid mixture via DEM simulation. First, according to a series of laboratory tests of sand-rubber mixtures, a systematic calibration framework is proposed to acquire the numerical parameters. Then, cubic compression tests are conducted with different rubber contents and confining pressures. The evolution of micro-scale properties, including the internal structure, stress network, and fabric anisotropy, is investigated to reveal the influences of rubber content and confining pressure on the micromechanical behaviors of sand-rubber mixtures. Through the investigation of the macroscopic responses, a unified hypoplasticity constitutive model is established and the relationships between the critical state parameters and rubber content are explored. The results show that the critical state shear strength of sand-rubber mixtures decreases with increasing rubber content and does not correlate with confining pressure. Additionally, the influence of rubber content on shear behaviors of SRMs is highly dependent on confining pressure, e.g., SRMs are more likely to exhibit soft-like behaviors under higher confining pressure. This study lays a foundation for the engineering design of geotechnical structures with an appropriate filling of the sand-rubber mixture. Moreover, this study also paves a viable way for a comprehensive investigation of other soft-rigid mixtures in the critical state.

Experimental verification of new neutron absorbers concepts

The presented paper describes experimental verification of the fixed neutron absorber for VVER-1000 fuel assemblies in the LR-0 zero-power reactor. This research determines the critical state parameters for fuel without these absorbers and for fuel with designed absorbers dedicated to the back-end of the fuel cycle and compares experimental data with the calculation. Several core configurations have been prepared, measured and evaluated. Two innovative forms of absorption materials were theoretically evaluated, then obtained and physically tested. From a neutronic and economic point of view, Gd2O3 and Sm2O3 in powder form were selected as absorber materials suitable for experimental verification. The reference calculation was realized with Serpent neutronic Monte Carlo code using ENDF/B nuclear data libraries.

Effect of coefficient of uniformity on cyclic liquefaction resistance of granular materials

Using three-dimensional discrete element method, we analyze the particle size distribution (PSD) effect on the cyclic liquefaction resistance of spherical particle assemblies. For the same mean particle size and log-linear type PSD, the coefficient of uniformity (Cu) is chosen as a descriptor of the PSD. Samples with five levels of Cu are isotropically compressed to the same pressure and two relative densities (Dr) informed by the maximum and minimum achieved void ratios determined for each Cu. The ten samples are subjected to constant volume cyclic simple shearing at different cyclic stress ratios until reaching initial liquefaction, in 56 simulations. The simulations suggest that at each Dr the evolution pattern of excess pore pressure ratio against the number of loading cycles normalized by the number of cycles to liquefaction is minimally affected by the Cu. For the samples with lower Dr, increasing the Cu in the range 1–3 first increases and then decreases the liquefaction resistance; this trend reverses at the higher Dr. Two critical state parameters based on the void ratio and the coordination number at the pre-shearing state of the samples correlate well with the cyclic liquefaction resistance for the ranges of Cu and Dr considered in this study.

Influence of grading and fabric arising from the initial compaction on the geomechanical characterisation of compacted copper tailings

Tailings dams constructed using the upstream method are generally less stable, because of its operational and constructive approach; this presents increased risks, which is the reason why such structures are being closed in Brazil. A feasible option to ensure the safety of closing operations in such dams consists of extracting tailings from behind the dam (reservoir), reducing moisture content through dewatering and compacting it into stable stacks. This demands knowledge of the compacted material's response. Thus, the present research assesses the mechanical response of compacted copper ore tailings extracted from two different sampling locations within the dam reservoir (i.e. about to be de-characterised) from northern Brazil. For this, drained and undrained triaxial compression tests were carried out on compacted dewatered dense, medium and loose specimens, which were assembled using the tailings retrieved from upper and lower beaches to evaluate the influence of grading, as well as the influence of the fabric arising from the initial compaction on the critical state lines (CSLs) of these saturated non-plastic silty sand tailings. The results indicated that the critical state parameters, in the υ–ln p′ space, are dependent on the fabric arising from the initial compaction. Distinct CSLs, which are all curvilinear and parallel to each other, were found in the research.

Deep Learning in the State of Charge Estimation for Li-Ion Batteries of Electric Vehicles: A Review

As one of the critical state parameters of the battery management system, the state of charge (SOC) of lithium batteries can provide an essential reference for battery safety management, charge/discharge control, and the energy management of electric vehicles (EVs). To analyze the application of deep learning in electric vehicles’ power battery SOC estimation, this study reviewed the technical process, common public datasets, and the neural networks used, as well as the structural characteristics and advantages and disadvantages of lithium battery SOC estimation in deep learning methods. First, the specific technical processes of the deep learning method for SOC estimation were analyzed, including data collection, data preprocessing, feature engineering, model training, and model evaluation. Second, the current commonly and publicly used lithium battery dataset was summarized. Then, the input variables, data sets, errors, and advantages and disadvantages of three types of deep learning methods were obtained using the structure of the neural network used for training as the classification criterion; further, the selection of the deep learning structure for SOC estimation was discussed. Finally, the challenges and future development directions of lithium battery SOC estimation using the deep learning method were explained. Over all, this review provides insights into deep learning for EVs’ Li-ion battery SOC estimation in the future.

Improved Particle Swarm Optimization-Extreme Learning Machine Modeling Strategies for the Accurate Lithium-ion Battery State of Health Estimation and High-adaptability Remaining Useful Life Prediction

To ensure the secure and stable operation of lithium-ion batteries, the state of health (SOH) and the remaining useful life (RUL) are the critical state parameters of lithium-ion batteries, which need to be estimated precisely. A joint SOH and RUL estimation approach based on an improved Particle Swarm Optimization Extreme Learning Machine (PSO-ELM) is proposed in this paper. The approach adopts Pearson coefficients to screen multivariate information of the discharge process as health indicators and uses them as inputs to enable accurate estimation of SOH and RUL prediction of lithium-ion batteries on the basis of the PSO-ELM model. The validity of the model is demonstrated by the NASA lithium-ion battery data set: the maximum root mean square error (RMSE) of the SOH estimation of the tested battery is 0.0033, the maximum RMSE of its RUL prediction is 0.0082, and the maximum absolute error of RUL prediction is one cycle number. In comparison with the prediction results of the traditional extreme learning machine, the optimized model proposed in this paper estimates the SOH of lithium-ion batteries and RUL with relatively high accuracy.

Experimental study on critical state behaviour of unsaturated silty sand under constant matric suctions

There are relatively few experimental studies on the hydromechanical and critical state behaviours of unsaturated silty sand. In this paper, suction-controlled, consolidated, drained triaxial shear tests were conducted on silty sand under saturated (net confining pressures of 100, 200, 300 and 400 kPa) and unsaturated (suctions of 30, 100 and 200 kPa and net confining pressures of 100, 200 and 300 kPa) conditions. For unsaturated silty sand, the effects of dry density, matric suction and net confining pressure on the hydromechanical and critical state behaviour were investigated, and the critical state parameters were obtained. The main findings for unsaturated silty sand included shear shrinkage at low dry density (1·6 g/cm3) and dilatancy at higher density (1·96 g/cm3). The peak shear strength was positively correlated with dry density, matric suction and net confining pressure. The critical state volumetric strain and critical state degree of saturation were negatively correlated with dry density and matric suction but positively correlated with net confining pressure. A new dilatancy equation that includes the state parameter for unsaturated silty sand was established. A unique critical state line passes through the origin in the effective stress [Formula: see text]–deviator [Formula: see text] plane, and its slope is the saturated critical state stress ratio [Formula: see text]. In the lnp*–v plane ([Formula: see text] is the specific volume), the critical state lines corresponding to different matric suctions are parallel.