Critical Depth Research Articles

Numerical analysis of shape coefficients and bearing capacity factors of shallow foundations on heterogeneous soil

We often face heterogeneous foundation soils in geotechnics, which significantly influence shallow foundations' shape coefficients and bearing capacity factors. The evaluation of these factors introduces significant uncertainties in the thickness of the upper layer is comparable to the width of the rigid footing placed on the soil surface. This ambiguity depends on the geometry of the footing, the mechanical properties of the soil, and other geotechnical factors. Conducting thorough geotechnical studies and performing specific analyses are essential to accurately assess the effect of clay layering on the shape coefficients and bearing capacity factors of circular and square footings. A numerical analysis using the FLAC 2D and 3D software is carried out to evaluate the effect of the superposition of two undrained clay layers on the bearing capacity and shape factors of circular and square footings subjected to a static axial load. The aspects of homogeneous and heterogeneous shear strength profiles were addressed at various positions of the height of the first clay layer. It was found that the critical depth of the first clay layer necessary to optimize the bearing capacity of a foundation resting on stratified soil is 2, 1.5, and 1, respectively, for strip, square, and circular footings. The shape coefficient values range between 1.14 and 1.22 for square footings and between 0.98 and 1.64 for circular footings. The results are compared to previously published values in the literature.

Investigation on the machining mechanism of silicon modified by Au ion irradiation in elliptical vibration diamond cutting

Single-crystal silicon (Si) has important applications in semiconductor, infrared optics, and photovoltaic industries. However, Si is difficult to be machined precisely due to its hard and brittle characteristics. Ion irradiation is proposed as an advanced technology to reduce the hardness and brittleness for a covalent crystal, which is beneficial for the ductile machining process. In the present research, the simulation and experimental investigation of Si with Au ion irradiation were carried out firstly. As following, the grooving experiment is carried out by elliptical vibration cutting (EVC). the machining performance is compared with ordinary cutting (OC) and the material removal mechanism is elaborated. The critical depth of cut for brittle-to-ductile transition is nearly 7 times higher by EVC compared to OC. Initial verification of material modification was conducted by Raman spectra and cutting microgrooves. Finally, the ion irradiation damage mechanism and amorphous Si (a-Si)/crystalline Si (c-Si) machining deformation mechanism were analyzed in detail by transmission electron microscopy. The irradiated sample contains an amorphous layer of 1050 nm, a transition layer containing dislocations and nanocrystals, and a fully crystalline layer. During machining a-Si/c-Si interface, the machining defects in the amorphous layer will first absorb the energy and ensure that the crystalline layer does not produce subsurface damage. In summary, ion-irradiated Si can be achieved in the amorphous region at any depth position and the substrate ductile machining without subsurface damage generation by EVC.

Brittle-ductile transition mechanism during grinding 4H-SiC wafer considering laminated structure

4H-SiC wafer with alloy backside layer is gradually applied in power devices. However, the laminated structure presents various challenges in manufacturing. In this study, a model for brittle-ductile transition in grinding of laminated materials is established and verified by grinding experiment to ensure the complete removal of the alloy backside layer while achieving ductile removal of the 4H-SiC layer. In the modeling process, the maximum unreformed chip thickness and brittle-ductile transition critical depth of each-layer in the laminated material is deriving, taking into account the laminated structure. Consider the variability in proportion of dynamic active grits during grinding, set operation is introduced to analyze the relationship between sets maximum unreformed chip thickness and brittle-ductile transition critical depth, and to predict the removal mechanism of the 4H-SiC layer. Comparing the predicted results with experimental grinding data, found that under the conditions of grinding wheel with average size of abrasive 10 μm, grinding wheel speed vs of 74 m/s, grinding depth ap of 10 μm, and feeding speed vw of 2 mm/s, the alloy backside layer can complete removal while achieving ductile removal of the 4H-SiC layer. This study provides a new method for predicting removal mechanism in grinding of laminated material and theoretical guidance for optimizing machining parameters of 4H-SiC wafer with alloy backside layer.

Numerical prediction of ground-borne vibrations due to continuous vibratory driving of circular closed-ended piles

Various types of pile driving work may induce high-intensity ground-borne vibrations. Predicting vibration intensity before adopting mitigation measures is vital for minimizing the impact of vibration on nearby structures and occupants. Vibratory pile driving is a commonly applied foundation construction method. However, numerical simulation models for ground vibrations during a complete process of vibratory driving have rarely been studied. This study introduces an axisymmetric finite element model that utilizes the arbitrary Lagrangian-Eulerian technique to simulate the continuous vibratory driving of a circular closed-ended pile penetrating from the ground surface to a target depth. The model validity was confirmed by assessing the calculated ground vibrations against the findings documented in earlier research. The results showed that the critical penetration depth of piles, at which the maximum peak particle velocity (PPV) occurs, varied with the radial distance and depth of points of interest, contradicting a common preconception. Moreover, the maximum PPV did not always occur on the ground surface across all radial distances. Parametric analysis revealed that an increase in the soil cohesion strength, pile diameter, or soil-pile friction, or a decrease in the driving frequency or soil damping ratio would increase ground vibrations due to vibratory pile driving.

Atomistic understanding of ductile-to-brittle transition in single crystal Si and GaAs under nanoscratch

Ensuring ductile removal in a grinding process is crucial for achieving the desired finish on a hard and brittle single crystal. This study provides new insights into the material removal processes in Si and GaAs single crystals, exploring their deformation behaviour using Berkovich and Conical tips to replicate contact from a fixed abrasive grit. Experimental observations are compared with Molecular Dynamic (MD) simulations to uncover the atomistic deformation mechanisms during the ductile-to-brittle transition (DBT). Notable plastic deformation and minimal cracking were consistently observed in Si, irrespective of the tips used. MD simulations supported this observation, revealing pronounced chip formation indicative of ductile material removal. The resistance to cracking in Si was attributed to amorphization induced by localized high contact stresses. In contrast, GaAs showed a propensity for cracking, with MD simulations revealing dislocation and slip band formation, and cracks emerging in the areas of substantial plastic deformation. These findings address phenomena not previously discernible in experimental studies due to the challenge of real-time observation. Moreover, the tip geometry was shown to significantly influence stress distribution, impacting deformation and crack formation in GaAs. This study also reveals limitations in predicting the critical depth for DBT in both Si and GaAs throught the amended Bifano, Dow, and Scattergood (aBDS) models and MD simulation, offering nuanced insights into these challenges that have not been extensively explored. It was found that the experimental results exceeded predictions by an order of magnitude. These discrepancies underscore the aBDS model's disregard for essential material properties and tip geometry, while the disparities between MD simulation and experiment are primarily attributed to the inherent limitations in the simulated length scales and challenges in detecting initial subsurface cracks.

Roof stability analysis for a shallow-buried cylindrical tunnel in Hoek-Brown rock strata

Roof stability of shallow-buried cylindrical tunnels in rock strata following the generalized Hoek-Brown criterion (GHB) is analyzed in this work. Based on the limit analysis method, a three-dimensional (3D) shallow-buried collapse mechanism for tunnel roofs is developed to derive various stability measures. Optimization codes are programmed to capture the optimal stability measure solutions. The effects of the 3D geometric characteristics, the rock mass strength parameters, and the buried depth on tunnel roof stability are investigated by a parametric analysis. The critical buried depth ratios corresponding to the transition between the shallow-buried and deep-buried tunnel roof collapse mechanisms are also presented. Thereafter a series of stability charts of the required supporting pressure and the factor of safety (FoS) is proposed for design purposes. This study provides a theoretical basis for design and engineering of tunnels with limited buried depth.

Origin of the anisotropic Beer–Lambert law from dichroism and birefringence in β -Ga2O3

The anisotropic optical absorption edge of β-Ga2O3 follows a modified Beer–Lambert law having two effective absorption coefficients. The absorption coefficient of linearly polarized light reduces to the least absorbing direction beyond a critical penetration depth, which itself depends on polarization and wavelength. To understand this behavior, a Stokes vector analysis is performed to track the polarization state as a function of depth. The weakening of the absorption coefficient is associated with a gradual shift of linear polarization to the least absorbing crystallographic direction in the plane, which is along the a-exciton within the (010) plane or along the b-exciton in the (001) plane. We show that strong linear dichroism near the optical absorption edge causes this shift in β-Ga2O3, which arises from the anisotropy and spectral splitting of the physical absorbers, i.e., excitons. The linear polarization shift is accompanied by a variation in the ellipticity due to the birefringence of β-Ga2O3. Analysis of the phase relationship between the incoming electric field to that at a certain depth reveals the phase speed as an effective refractive index, which varies along different crystallographic directions. The critical penetration depth is shown to be correlated with the depth at which the ellipticity is maximal. Thus, the anisotropic Beer–Lambert law arises from the interplay of both the dichroic and birefringent properties of β-Ga2O3.

The study on the coupled influence of water saturation on heat and mass transfer processes within porous media under CW laser irradiation

Continuous wave (CW) laser irradiation induces temperature changes in various phases within porous media, accompanied by phase change and gas transport. Water saturation is a crucial factor influencing this context's moisture and heat transfer process. This paper addresses this issue by establishing a theoretical model for CW laser irradiation on unsaturated porous media. Through experiments and simulations, it studies the effects of different water saturations on heat and mass transfer under laser irradiation. The results indicate that the critical depth reflects the influence of water saturation under laser irradiation on the distribution of solid-phase temperature in both time and space dimensions. Specifically, an increase in water saturation enhances the uniformity of solid-phase temperature distribution, while the gas temperature exhibits a similar distribution pattern. For mass transfer processes, it increases the evaporation rate and Darcy velocity of porous media within the effective range of laser irradiation. Lower water saturation facilitates phase change processes and accelerates gas transport rates. Importantly, this trend remains consistent even with the emergence of dry-saturation zones. Additionally, the decrease in water saturation has a coupled promoting effect on gas temperature and mass transfer processes. Lowering water saturation can increase gas temperature and consequently enhance mass transfer processes. Simultaneously, enhancing mass transfer processes benefits heat exchange between the two phases. In the four sets of experiments, the conformity of the surface temperature rise curves obtained from experiments and simulations is good, indicating that the model can accurately reflect the temperature rise patterns of sand particles. In summary, this work provides valuable research results on the effects of different water saturations on laser irradiation-induced temperature rise, phase change, and gas and moisture transport within porous media. It lays a specific theoretical foundation for laser soil remediation technology.

Sea level and East Asian winter monsoon-controlled periodic transition of sinks in fine-grained sediments in the East China sea over the past 200 kyr

The study of critical geological processes of sediments from source to sink in the East China Sea (ECS) is of great significance for further understanding the surface processes, material cycling, and sedimentary evolution in the East Asian continental margin. Based on the high-resolution clay mineralogy and REEs in fine-grained sediments of Core CSHC-15, this study has analyzed the periodic transition mechanism of sinks in fine-grained sediments in the ECS from a source-to-sink perspective. The clay mineral provenances of Core CSHC-15 exhibited distinct periodic abrupt shifts between the Changjiang and Taiwan island over the past 200 kyr, indicating the periodic transitions of sinks in fine-grained sediments between the inner shelf of the ECS and the Okinawa Trough. When the sea level rose or fell to a critical depth (around −25 m or −50 m), the changes in the accommodation space of the continental shelf and the shelf fronts were the direct factors leading to the periodic transitions of sinks in fine-grained sediments in the ECS. The intense eccentricity cycles (100-kyr) of the clay mineral parameters of Core CSHC-15 reflected the impacts of the East Asian Winter Monsoon (EAWM). This study confirms that long-term (eccentricity and longer cycles) climate signals of the source areas can be extracted from the clastic sedimentary records of the ECS. The new finding highlights the periodic transition mechanism of sedimentary sinks in the ECS that will promote the progress of sedimentary geology since the Late Quaternary.

Effect of Friction on Critical Cutting Depth for Ductile–Brittle Transition in Material Removal Mechanism

Abstract The material removal process takes place due to phenomena such as plastic deformation and brittle fracture. A long continuous chip is formed when the plastic deformation dominates, whereas a fracture-induced discontinuous chip is formed when the brittle fracture dominates. The means of material removal changes at a certain cutting depth for a particular material, the so-called transition depth of cut (TDoC). This article aims to predict the TDoC while including the effect of friction between the tool and workpiece. We propose a modification to a recently developed model (Aghababaei et al., 2021, “Cutting Depth Dictates the Transition From Continuous to Segmented Chip Formation,” Phy. Rev. Lett., 127(23), pp. 235502) to incorporate the effect of friction. The model predicts a transitional depth of cut as a function of tool geometry, material properties, and friction. The model is supported by performing orthogonal cutting experiments on different polymers such as polymethyl methacrylate (PMMA), polyoxymethylene (POM), and polycarbonate (PC). The model is also compared with existing models in the literature, where an improvement in the prediction of TDoC is shown. Moreover, the effect of the friction coefficient and rake angle on the TDoC is discussed. The results show that transitional cutting depth is reduced by increasing the friction coefficient. Alternatively, the TDoC reaches its maximum at an optimum rake angle, which is a function of the specific material being cut. The model aids in accurately predicting the TDoC, a crucial factor for optimizing various material removal processes.

Shallow-landslide stability evaluation in loess areas according to the Revised Infinite Slope Model: a case study of the 7.25 Tianshui sliding-flow landslide events of 2013 in the southwest of the Loess Plateau, China

Abstract. The occurrence of shallow loess landslides induced by prolonged heavy rainfall is prevalent in loess-dominated regions, often leading to property damage, human casualties, and sediment pollution. Developing an accurate prediction model for shallow landslides in loess areas is crucial for effective landslide mitigation. In 2013, prolonged heavy rains from 19–25 July triggered mass sliding-flow loess landslides in Tianshui, China. Landslide data, along with the characteristics of the sliding-flow loess landslides, were obtained through extensive field investigations and remote sensing interpretations. The sliding-flow loess landslide event demonstrated clustering, high density, small areas, and long travel distance. The depth of the sliding surface is correlated with the saturated layer resulting from rainfall infiltration; it is typically less than 2 m deep and negatively correlated with slope steepness. Based on the common characteristics of shallow loess landslides, the mechanisms involved in the sliding-flow landslide are proposed. The Revised Infinite Slope Model (RISM) was introduced using an equal differential unit method to address deficiencies when the safety factor remains constant or increases with increasing slope greater than 40°, as calculated using the Taylor slope infinite model. The relationship between the critical depth and the slope of the shallow loess landslide was determined. The intensity–duration (I–D) prediction curve of the rainfall-induced shallow loess landslides for different slopes was constructed and combined with the characteristics of rainfall infiltration for use in forecasting regional shallow loess landslides. Additionally, the influence of loess strength on the shallow loess landslide stability was analyzed. The shallow loess landslide stability responds to slope and cohesion but is not sensitive to the internal friction angle.

The adjustable adhesion strength of multiferroic composite materials via electromagnetic loadings and shape effect of punch

Tunable and reversible dry adhesion possess great potential in a wide range of applications including transfer printing, climbing robots, wearable devices/electronics, and gripping in pick-and-place operations. Multiferroic composite materials offer new routines and approaches to achieve tunable adhesion due to their multi-field coupling effects. In this paper, the classical Johnson-Kendall-Roberts (JKR) adhesion model is extended to investigate the adhesive contact problem of a multiferroic composite half-space indented by an axisymmetric power-law shaped punch, whose shape index is denoted by n. The JKR-n adhesion models under the action of the power-law shaped punches with four different electromagnetic properties are set up by means of the total energy method. The explicit analytical expressions relating the indentation load and indentation depth to the contact radius are obtained, which can include the existing results in open literature as special cases. The generalized Tabor parameter and the interfacial adhesion strength applicable to multiferroic composite materials are defined. The effects of the shape index and the electromagnetic loadings on adhesion behaviors are revealed. It is found that both of them have prominent influences on the relationships among the indentation load, indentation depth and contact radius, the contact radius and indentation depth at self-equilibrium state, and the critical contact radius and indentation depth at pull-off moment. The pull-off force under the action of the conducting spherical punch subjected to non-zero electromagnetic loadings is dependent on material properties, which is different from the classical JKR result. More importantly, our analysis indicates that the pull-off force and the interfacial adhesion strength can be adjusted via altering the electromagnetic loadings and the shape index of the punch, which provides new approaches to achieve tunable adhesion.

Modeling and analysis of surface integrity transition in cutting of Sip/Al composites based on coordination deformation effect of particle-matrix

With the wide application of Sip/Al composites in key fields, it is critical to understand the material removal behavior and surface integrity evolution mechanism of Sip/Al composites. In this paper, based on the nanoindentation and scratching experiments, the coordination deformation behavior of Si particles and the Al matrix were investigated at the micro-scale, and the mechanism and conditions of surface integrity transition (SIT) of Sip/Al composites were elucidated. Then, taking into account the feature of particle fragmentation and detachment caused by interfacial failure, an analytical model of specific cutting energy for Sip/Al composites cutting under different material removal modes was established. The competitive relationship between ductile deformation and surface defect formation was investigated, and a quantitative prediction model for the critical depth of SIT was proposed. The results show that the evolution of the material removal behavior of Sip/Al composites is a consequence of the coordination deformation the Al matrix and Si particles. The material removal mode of Sip/Al composites transitions from ductile removal to quasi-brittle removal with particle fragmentation and detachment, and there is an obvious SIT characteristic. The prediction results of critical depth are in agreement with the experimental results, with an average error of less than 9.8 %. Moreover, an appropriate increase in cutting speed can effectively enhance the surface integrity of Sip/Al composites. This research contributes to a deeper understanding of the low-damage machining mechanism of Sip/Al composites.

Scratching properties of 4H–SiC single crystal after oxidation under different conditions

Single-crystal silicon carbide (SiC) has poor machinability because of its low fracture toughness, and surface modification has become the first choice for SiC polishing to obtain a high removal rate and a smooth surface. However, the removal mechanism of SiC after modification remains unclear. In this study, diamond scratching experiments were performed on 4H–SiC after oxidation under two conditions. To reveal the material removal mechanism, the scratch morphology and subsurface defects were analysed using Raman spectroscopy, X-ray photoelectron spectroscopy, scanning electron microscopy, and transmission electron microscopy. The results showed that oxidation improved the scratch depth and critical depth for ductile removal, resulting in a smooth scratch surface with low damage. However, weak oxidation increased the median crack length and exacerbated the subsurface damage. The SiOxCy, C = O, C–O–C, and Si–O–Si functional groups produced during oxidation reduced the hardness and improved the machinability of the 4H–SiC substrate. On the other hand, strong oxidation reduced the generation of surface cracks, tearing, and spalling, and weakened the propagation of subsurface median cracks. These results prove that ultrasonic-assisted photocatalytic oxidation provides high removal efficiency and defect control, providing a new approach for the synergistic polishing of SiC substrates.

Artificial intelligence and depth ontology: implications for intercultural ethics

Abstract Despite increasing concerns over the use of AI in surveillance, privacy, public health, climate change, global migration and warfare, the implications of its use in the field of intercultural communication are still not clearly defined. This paper critically examines the contemporary emergence of AI through the lens of a critical realist depth ontology to argue that AI, with its unending interplay of signs and symbols, is the ultimate simulacrum. As such, AI vacates the normative terrain of judgemental rationality in favour of the relativist terrain of endless simulacra and the fetish appearances of postmodernism. To illustrate this, it is argued that the inability of AI to make judgements based on judgemental rationality (or Ethics1) occludes the possibility of intervening in the world to ameliorate real injustice. Therefore, if intercultural ethics remains within the realm of judgmental relativism (or Ethics2) it abdicates the possibility to have an impact in the material world.

Assessing the Impact of Climate Change on Glacial Lake Outburst Flood (GLOF) in Eastern Hindu Kush Region Using Integrated Geo-Statistical and Spatial Hydrological Approach

Glacier retreat, a major impact of climate change that continues to occur in many parts of the world, continues to increase the risk of glacial lake outburst floods (GLOFs) in northern Pakistan. The rapid melting of glaciers in the mountains of Northern Pakistan, including the Hindu Kush, the Himalayas and the Karakoram, the rapid melting of glacier has led to the formation of 3044 glacial lakes, with 33 identified as particularly vulnerable to GLOFs. This study uses remote sensing and geographic information systems (GIS) methods for mapping and representing GLOFs. Based on the observational data of lake area, volume, and depth, empirical equations are developed through statistical methods. Only two lakes, Chitral-GL2 and Swat-G31, are classified as lakes with high potential for GLOF. Through modeling techniques using HEC-RAS and HEC-GeoRAS spatial hydrological models integrated with GIS remote sensing, the spatial extent and depth of inundations under different lake volumes are assessed. The analysis reveals that a total area of 20.56 km2 is susceptible to submersion by GLOFs, with Chitral-GL2 flooding area of 14.80 km2 and Swat-GL31 5.79 km2. Different land types are impacted by critical water depths, with built-up and agricultural lands 2.7 km2 totally, and barren lands 8.93 km2 under different flood depths ranging from less than 5 m to over 15 m.

Anisotropy Dependence of Material Deformation Mechanisms in Nanoscratching Monocrystalline BaF2: Experiments and Atomic Simulations.

Monocrystalline barium fluoride (BaF2), known for its exceptional optical properties in the infrared spectrum, exhibits anisotropy that influences surface quality and material removal efficiency during ultraprecision machining. This research explores the impact of anisotropy on the deformation and removal mechanisms of monocrystalline BaF2 by integrating nanoscratch tests with molecular dynamics (MD) simulations. Nanoscratch tests conducted on variously oriented monocrystalline BaF2 surfaces using a ramp loading mode facilitated the identification of surface cracks and a systematic description of material removal behaviors. This study elucidates the effect of crystal orientation on the ductile-brittle transition (DBT) of monocrystalline BaF2, further developing a critical depth prediction model for DBT on the (111) crystal plane to reveal the underlying anisotropy mechanisms. Moreover, nanofriction and wear behaviors in monocrystalline BaF2 are found to be predominantly influenced by scratch direction, crystal surface, and applied load, with the (110) and (100) planes showing pronounced frictional and wear anisotropy. A coefficient of friction model, accounting for the material's elastic recovery, establishes the intrinsic relationship between anisotropic friction and wear behaviors, the size effect, and scratch direction. Lastly, MD modeling of nanoscratched monocrystalline BaF2 reveals the diversity of dislocations and strain distributions along the (111) [-110] and [-1-12] crystal directions, offering atomic scale insights into the origins of BaF2 anisotropy. Thus, this study provides a theoretical foundation for the efficient processing of fluorine-based infrared optic materials exhibiting anisotropy.

Technology and technical means for the implementation of reproduction methods for soil fertility

Soil fertility is determined by the presence of humus as the main part of organic matter. The extended reproduction of soil fertility is ensured by the introduction of organic and mineral fertilizers, the cultivation of sidereal crops and the decomposition of plant residues. (Research purpose) The research purpose is developing the technologies and means of mechanization for extended reproduction of fertility. (Materials and methods) For the joint application of liquid organic fertilizers and the cultivation of siderates, a unit has been developed that implements a hose technology for transporting liquid organic fertilizers. Fertilizers are fed through pressure hose lines to the working parts deep into the soil layer. The combined unit consists of a tractor K-744 Kirovets and an adapter for deep tillage with liquid fertilizers, as well as a seeder for small-seeded crops. To level the surface of the field after the passage of the unit and the sealing of the sown seeds of the sideral culture, the unit is equipped with a tooth roller. (Results and discussion) Formulas for determining the critical processing depth are given, the power calculation of the unit is performed. The design of the tillage tool allows to install flat-cutting working parts with a grip of 0.80 meters and slits with a grip of 0.45 meters. Tests of the combined unit were carried out. The depth of tillage was 36±1 centimeters, the seeding rate of the sideral crop (oilseed radish) was 25 kilograms per hectare, the operating speed range of the unit was from 0.4 to 0.8 meters per second. (Conclusions) The uniformity of the subsurface distribution of organic fertilizers was 90-95 percent. The specific energy intensity of the technological process of the combined unit based on the K-744 tractor for intra-soil fertilization is 40-65 kilowatt hours per hectare (excluding the capacity for pumping fertilizers). Energy consumption depends on the depth of cultivation and resistivity of the soil. The proposed method allows preventing water and wind erosion of the soil, improving its agronomically valuable properties. Reducing the pesticide load on the soil and its microflora contributes to the transition to a model of sustainable agroecosystems, improving and improving crop quality. The proposed technology provides extended reproduction of soil fertility.

Dynamics of Ring Dark Solitons and the Following Vortices in Spin-1 Bose–Einstein Condensates

Abstract This work focuses on the evolution behaviors of ring dark solitons (RDSs) and the following vortices after the collapses of RDSs in spin-1 Bose-Einstein condensates. We find that the weighted average of the initial depths of three components determines the number and motion trajectories of vortex dipoles. For the weighted average of the initial depths below the critical depth, two vortex dipoles form and start moving along the horizontal axis. For the weighted average depth above the critical depth, two or four vortex dipoles form, and all start moving along the vertical axis. For the RDS with weighted average depth at exactly the critical point, four vortex dipoles form, half of the vortex dipoles initiate movement vertically, and the other half initiate movement horizontally. Our conclusion is applicable to the two-component system studied in earlier research, indicating its universality.

Explicit finite element simulations of dynamic low adhesion behavior between wheel and rail in the presence of high-frequency vibrations

PurposeDynamic low adhesion (DLA) has become an urgent problem for the high-speed wheel-rail system because of continuous decrease of adhesion redundancy in the past decades. This article aims to provide a simulation method to reveal the mechanism of DLA under high-frequency vibrations.Design/methodology/approachA transient wheel-rail rolling contact model is developed for a typical Chinese high-speed railway system using the explicit finite element (FE) method. Instantaneous adhesion exploitation levels are studied in the time domain, for which driving cases over corrugated rails are taken as an example. A speed up to 500 km/h is considered together with different traction coefficients and corrugation dimensions. DLA is expected when the instantaneous adhesion exploitation level reaches 1.0, that is adhesion saturates and full sliding contact occurs.FindingsThe instantaneous adhesion exploitation level can be very high in the presence of corrugation, even at low traction coefficients. DLA is found to occur as great vertical unloading takes place and causes a significant increase of creepage. An approach is further developed to determine the critical depth of corrugation over which DLA occurs.Originality/valueThis study employs the transient wheel-rail rolling contact model to predict the instantaneous adhesion exploitation level under high-frequency vibrations. The presented results reveal a mechanism of DLA being beneficial to guidelines for future railway practice.