Internal Energy Dissipation Research Articles

Impact and erosion dynamics of inclusion-enriched dry granular flows on rigid barriers with basal clearance: Numerical insights from hybrid MP-DEM simulations

Rigid barriers with basal openings are often installed along predicted flow paths to protect downstream facilities from dry granular flows containing large boulders. However, current design practices do not consider the effects of these inclusions during impact, discharge, overflow, and bed erosion. We conducted hybrid MP-DEM simulations to study the dynamics of dry sand flow with inclusions impacting a rigid barrier with a basal opening. Our findings show that accounting for large inclusions is crucial for barrier design, as they alter dry granular flow regimes, delay dead zone formation, and affect overflow dynamics. Current analytical solutions may overestimate velocity attenuation by up to 60% if inclusions are not considered. A 10% increase in inclusion volume fraction leads to 6%-28% increases in internal energy dissipation during overflow, resulting in an overflow distance 20% lower than existing predictions. Additionally, channel bed erosion due to landing flow with inclusions creates a flow depth up to 3.5 times thicker than at the first barrier location. This suggests that using the initial flow depth for impact force assessment on a second barrier may not be conservative for erodible channel beds and inclusion-enriched flows.

Blade redesign based on inverse design method for energy performance improvement and hydro-induced vibration suppression of a multi-stage centrifugal pump

As the urgency of the global energy crisis escalates and environmental protection standards become more stringent, the industrial sector is placing increased emphasis on enhancing energy efficiency and advancing vibration control technologies. Within this context, multi-stage centrifugal pumps (MSCPs), pivotal in energy systems, play a crucial role in influencing both system performance and environmental impact. This paper embarked on employing an inverse design method (IDM) to innovate the redesign of MSCP blades, introducing a steady-state index for characterizing the intensity of unsteady pressure fluctuations, thereby streamlining optimization costs. Optimization techniques utilizing an artificial neural network model and a multi-objective evolutionary algorithm were employed to achieve an optimal balance between maximizing energy efficiency and reducing hydro-induced vibrations. The optimized MSCP enhanced not only boosting performance but also a 2.75 % increase in weighted efficiency, significantly widening the high-efficiency operation zone. The improvement in vibration characteristics was manifested by an average reduction of more than 25 % in the amplitude of the primary frequency of pressure pulsations within the double volute, with a maximum reduction reaching 50.9 %. Furthermore, the research delved into the analysis of the internal energy dissipation mechanisms of MSCPs, drawing upon the entropy production theory and the enstrophy concept. This analysis reveals that energy dissipation in the mainstream zones is predominantly affected by shear enstrophy, whereas, in the wall regions, it is primarily governed by fluid velocity. The comprehensive performance enhancement of the optimized model is significantly credited to the refinement of the blade profile.

Ultrahigh-efficiency X-ray energy dissipation enabled by the integration of core–shell photon nanotraps and hierarchical natural leather

The widespread application of high-energy X-ray radiation has prompted improvements in the performance of radiation-protection materials. Currently, achieving enhanced X-ray shielding efficiency and minimized surficial photon scattering remains challenging when using traditional strategies. In this study, an ultrahigh-efficiency X-ray energy absorption strategy and mechanism are proposed by integrating Bi@Gd core–shell photon nanotraps into the hierarchical fibrous network of natural leather (Bi@Gd/NL), and the surficial-energy-transfer energy-attenuation mechanism of the traditional strategy was successfully transformed into internal-energy-dissipation. The proposed strategy could induce high-energy photons into a porous structure composed of hierarchical microfibers and nanofibers to reduce surface-scattered secondary radiation, and the well-assembled high-atomic-number core–shell nanotraps can trap photons within the structure and facilitate collisions and subsequent internal energy dissipation to improve the shielding capabilities. Our analysis shows that Bi@Gd/NL with 1.40 mmol cm−3 Bi and 0.11 mmol cm−3 Gd exhibits superior shielding performance against X-rays, comparable to that of a 0.25-mm Pb plate. More than 99.95 % photon energy is dissipated within the nanotraps, and the surficial scattering of photon is considerably lower than that of materials fabricated using the traditional strategy, indicating that the ionizing radiation hazards are successfully suppressed. Simultaneously, the developed materials demonstrate exceptional wearability, with a density of only 1/10 that of Pb, as well as outstanding flexibility, physiomechanical strength, and irradiation stability. This proposed strategy and mechanism provide important guidance and insights on the development of novel absorption-type shielding materials for protecting ionizing radiation-related individuals and environments.

Spatial and Temporal Variability of Turbulent Mixing in the Deep Northwestern Pacific

AbstractSmall‐scale turbulent mixing supplies potential energy for the upwelling of deep waters in the abyssal ocean, a key component of the global overturning circulation. This process is particularly significant in critical regions such as the Northwestern Pacific where the upwelling structure of deep waters remains poorly understood due to limited knowledge of deep ocean mixing. Here, we investigate the full‐depth spatiotemporal variability of turbulent mixing in the deep Northwestern Pacific based on hydrographic data collected over repeated surveys. Nineteen‐year‐average diapycnal diffusivity of 1.42 × 10−4 m2 s−1 is reveled in the deep Philippine Sea, indicating significantly stronger mixing compared to the stratified ocean interior. Spatially, turbulent mixing strengthens toward the bottom and intensifies westward from the open Pacific to the Philippine Sea due to rough topography. At certain mixing hotspots, enhanced mixing can penetrate up to 2,500 m above the bottom, suggesting a substantial potential for upwelling. Below 2,000 m, turbulent mixing exhibits pronounced seasonal variation that deep mixing is more intense in summer (winter) than in winter (summer) in the West Caroline Basin (the Parece Vela Basin). This spatially varying seasonality may be attributed to the inhomogeneous internal tidal energy dissipation in the Northwestern Pacific. Our study will serve to clarify the modulation of turbulent mixing to deep‐water mass transformation and circulation in the Northwestern Pacific.

Mechanism of the impact of sediment particles on energy loss in mixed-flow pumps

Numerical simulations were performed on the fluid domain of the mixed-flow pump with different solid-phase volume fractions to examine the influence of the sediment particles on internal energy dissipation. The energy properties of the mixed-flow pump were analyzed using the entropy production theory, considering the various flow rates and the solid particle conditions. The research examined the impact of the proportion of the solid particles in the flow on the performance and effectiveness, uncovering the complexities of the energy dissipation in the channel. The results showed that incorporating solid particle media resulted in the decrease in both the performance and effectiveness of the mixed-flow pump compared to water conditions. The mixed-flow pump's head decreased by 0.56 % and its efficiency declined by 2.74 % due to the change in particle volume fraction (Cv) from 5 % to 7.5 %. Upon transitioning from Cv = 7.5 % to Cv = 10 %, the head exhibited a 2.54 % decrease, coupled with a 7.22 % efficiency reduction, signifying pronounced energy loss. The findings highlight that the increase in the quantity of the solid particles enhances the pump's energy dissipation. Solid particles tend to be mainly concentrated in the impeller inlet, blade outer edge, guide vane inlet, and guide vane outer edge regions at varying solid-phase volume fractions. The main dissipation in the fluid region of the mixed flow pump mainly occurs in the impeller and the guide vane, the total energy loss in the guide vane is more than 500 W under the three volume fractions, the total energy loss in the impeller is also about 500 W, and the inlet and outlet losses are small. These research outcomes lay the groundwork for further enhancements in the energy characteristics of mixed-flow pumps.

Vibrations of viscoelastic FG porous graphene-platelets reinforced doubly-curved shells via experimental characterisation of graphene platelets

This work explores the vibrations of viscoelastic functionally-graded (FG) porous graphene-platelets reinforced doubly-curved shallow shells via experimental characterisations of graphene platelets. In particular, the effects of ultrasonication time of graphene platelets, on the vibrations of graphene-platelets reinforced shells, are studied. This is of interest because graphene platelets are often ultrasonicated in solvents to achieve better dispersions during the fabrication of graphene-platelets/epoxy composite structures. In this study, geometric characteristics of the graphene platelets under different sonication times are quantitatively and qualitatively analysed through experimental characterisation techniques, including a laser diffraction particle size analyser, a scanning electron microscopy (SEM), and a scanning force microscopy (SFM). The geometric characteristics of graphene platelets are considered in the effective material properties using a micromechanics model of Halpin-Tsai. Different FG distributions of graphene platelets and closed-cell porosity are modelled. The Kelvin-Voigt viscoelastic model is used to consider the internal friction-induced energy dissipation for the polymeric composite shell. Hamilton’s variational principle and an assumed mode method are used to derive and solve the equations of motion, respectively, for the vibrations of the doubly-curved shells. The effects of graphene platelets sonication time, in combination with the effects of graphene platelets weight fraction, porosity coefficient, FG distributions, shell thickness ratio, and shell curvature radii, are scrutinised. The results show that increasing ultrasonication time reduces the shell’s out-of-plane dimensionless fundamental frequency as a result of the reduction in graphene platelets aspect ratio.

Analytical Solution for Seismic Stability of 3D Rock Slope Reinforced with Prestressed Anchor Cables

Currently, the study of analytical solutions for the seismic stability of slopes under anchorage conditions is one of the hottest subjects in engineering. In this paper, an analytical solution for the seismic safety of the three-dimensional (3D) two-stage rock slope reinforced with prestressed anchor cables governed by the nonlinear Hoek–Brown criterion was deduced, in which the analyses of seismicity were performed by the latest modified pseudo-dynamic method. This method supplements the consideration of the damping effect of the rock medium on seismic waves, which is more in line with the real seismic situation. A mathematical geometric model was developed for calculating the external forces work and internal energy dissipation acting on 3D rotating rock masses reinforced with prestressed anchor cables, in which the seismic work rate was calculated using a new layer-by-layer superposition summation method. The analytical solution of the safety factor could be collated as an explicit function of several variables, and then, the optimal value was obtained by the Particle Swarm Optimization (PSO) algorithm. To corroborate the accuracy of new analytical solutions, the results were contrasted with those of the pertinent literature. The results of the two comparisons were very close. Ultimately, the sensitivity analyses and coupling effects of seismic pseudo-dynamic factors and prestressing anchorage factors were carried out. It was found that even small seismic intensities had a large effect on the stability of rock slopes with developed joints. Increasing the number of steps and prestressing anchors can effectively improve the stability of rock slopes under seismic effects. The conclusions have significant implications for the anchorage design of the 3D two-stage rock slope as seismic events occur.

Finite element analysis of locally strengthened stainless-steel tube under lateral impact loading

In this study, a Finite Element (FE) model of locally strengthened high-strength stainless-steel tube subjected to lateral impact loads is established using LS-DYNA to investigate its dynamic behaviours. The accuracy of the FE results is verified by comparing with the test results. The impact force, bending moment, stress and strain responses as well as the internal energy dissipation histories of the strengthened tube are analysed during the entire impact process. The results indicate that the impact resistance of the strengthened tube is obviously enhanced as compared to hollow stainless-steel tube. Furthermore, parametric studies are conducted to reveal the influence of axial compressive force, impact position, impact velocity and material strength on the impact behaviour of the strengthened tube. The results show that the application of axial compressive force reduced the impact force and increased the deformations of the strengthened tube. The impact resistance of the strengthened tube performed an increasing trend when moving the impact position towards the support and increasing the material strength. In addition, the increase of impact velocity significantly reduced the impact duration. Finally, design recommendations and process were proposed to facilitate the application of locally strengthened tube.

Protection performance of aluminum matrix ceramic ball composite materials plate for hypervelocity impact based on FE-SPH adaptive method

Space debris is a major threat to the safety of spacecraft in orbit, and advanced protective materials with lightweight and high impact resistance are effective passive protection solutions. In order to investigate the hypervelocity impact protection performance of aluminum matrix ceramic ball composite materials plate, this paper has carried out the hypervelocity impact test of aluminum matrix ceramic ball composite materials plate, and verified the accuracy of the numerical model based on the FE-SPH adaptive method, and then carried out a comparative study on the hypervelocity impact protection performance of aluminum plate and aluminum matrix ceramic ball composite materials plate with the same area density. The results show that: compared with the aluminum plate conditions, the composite materials plate has a better ability to broken the projectile. Compared with the aluminum plate, the kinetic energy absorbed by the composite materials plate is increased by 37.04%, and the kinetic energy of the generated debris cloud decreased by 69.57%. The proportion of the internal energy dissipation of the composite materials impact system reaches up to 72.03%. The secondary pollution generated by the composite materials plate is less and the hazardous debris have less threat to the rear wall. The research in this paper can provide reference for the selection of hypervelocity impact protection materials.

Numerical and experimental studies on the carcass characteristics of a radial tire

In this research, the carcass characteristics of a radial tire were analyzed by performing numerical simulations on ABAQUS software based on the single factor control variable method, and the feasibility of the proposed numerical model was verified by executing experiments on a tire uniformity testing machine. It was found that when the tire crossed the bump, the preload had positive effects on the internal energies and friction–dissipation fluctuation of the tire, but had little influence on its kinetic energy fluctuation. Tire speed was positively correlated with the fluctuation of kinetic energy, but negatively correlated with the friction–dissipation fluctuation of the tire. In addition, there was a slight correlation between the speed and the internal energy fluctuation of the tire. Moreover, the change in the tire pressure had little influence on the kinetic energy, internal energy, and friction dissipation of the tire.

Dynamical analysis of a ferrofluid subjected to oscillatory field and shear rates: Applications to magnetic hyperthermia

The dynamical magnetic response of a small sample of ferrofluid is investigated numerically. A validated in-house research code is used to compute the translational and rotational motion of the particles. This code uses a robust scheme of Ewald summation to compute long-range periodic torques and forces between the particles. The model of the ferrofluid consists in a suspension of magnetic hard spheres replicated in lattices to ensure the convergence of the system’s transport properties. Ensemble averages over several realizations for each simulation are carried out. The suspension is subjected to field and shear time-dependent excitations. The effect of magnetic hyperthermia is evaluated by the average rate of internal energy dissipation due to an oscillatory magnetic field and oscillatory shear rate. Nonlinear dynamical tools such as phase spaces and Poincaré maps are applied to interpret the dynamical behavior of the suspension. Results show that when the suspension reaches its saturation magnetization due to a delayed time-response of the particles the internal energy dissipation decreases with respect to the local applied field. The Poincaré maps reveal that in dilute regimes the system presents quasi-periodic behavior for an alternating magnetic field. Also, the application of an oscillatory shear-rate increases the bulk internal energy of the system due to the magneto-viscous effect, even though it diminishes the internal area of the hysteresis loop. This work brings a better understanding of the dynamical response of ferrofluids that could be useful in magnetic hyperthermia applications.

Numerical investigation of no-load startup in a high-head Francis turbine: Insights into flow instabilities and energy dissipation

The presented paper numerically investigates the internal flow behaviors and energy dissipation during the no-load startup process toward a Francis turbine. Passive runner rotation is implemented through the angular momentum balance equation accompanied by dynamic mesh technology and user defined function. Three phases of rotational speed are identified: stationary, rapid increase, and slow increase. Head exhibits a monotonic decrease, rapid rise and fall, and eventual fluctuation. Flow rate shows quasi-linear increase. The pressure fluctuations in the vaneless region are primarily dominated by the frequencies induced by Rotor-Stator Interaction and a broad frequency range below 50 Hz, and below 30 Hz in the draft tube. Runner inlet experiences positive to negative incidence angles, causing intense flow separation and unstable structures. Draft tube exhibits large-scale recirculation and evolving vortex structures. Energy loss analysis based on the entropy production method highlights the runner and draft tube as primary contributors. The energy loss within the runner exhibits an initial increase, subsequent decrease, and then a rise again during the stationary and rapid speed increase phases. While the draft tube shows a rapid increase during the phase of rapid speed increase. Turbulent fluctuations significantly contribute to entropy production loss, with trends matching total entropy production. Maximum energy loss locations correspond to runner inlet and draft tube wall, emphasizing the importance of unstable flow and vortex generation. This study establishes foundational insights into unstable hydrodynamics and energy dissipation modes during hydraulic turbine no-load startup, paving the way for further research.

Investigation on unstable flow characteristics and energy dissipation in Pelton turbine

The internal flow scale of a Pelton turbine is variable, and the interaction between the jet and the bucket has strong transient characteristics, resulting in an incomplete understanding of its internal vortex structure evolution and energy dissipation mechanisms. In order to reveal the influence of vortices on the flow regime and energy dissipation mechanisms in the turbine, this paper establishes the correlation between the unsteady flow characteristics and energy dissipation inside the Pelton turbine based on the energy balance equation and quantifies the energy losses inside the turbine. The results indicate that vortex structures present a non-uniform distribution inside the jet, which disrupts the uniformity of the jet velocity distribution, resulting in an uneven distribution of high-vorticity zones on the bucket surfaces and intensifying flow interference among the buckets. The strong shear flow caused by the downstream flow detachment of the needle guide, the turbulent boundary layer on the jet surface, and the wake effect downstream of the needle tip are the main reasons for the dissipation of fluid kinetic energy. The distribution range of energy loss on the rotating bucket closely corresponds to the position of the high-vorticity zone. Energy dissipation inside the turbine is primarily in the form of turbulent kinetic energy, and the injectors and runner are the primary energy dissipation components. Moreover, inside the injectors, each form of energy loss remains relatively constant, whereas inside the runner, its rotation induces fluctuating energy losses attributed to Reynolds stress work. The results contribute to an enhanced understanding of the energy dissipation characteristics and complex flow mechanisms within the turbine, providing reference for the optimisation and efficient operation of the multi-nozzle Pelton turbine.

Influence of tip clearance on internal energy loss characteristics of axial flow pumps under different operating conditions

Axial flow pumps possess a unique structure where there must be clearances between the impeller and the piping wall, usually not exceeding 0.1% of the impeller diameter. Despite the small size of the clearance, the internal micro-vortex structures have a non-negligible impact on the main flow field of the impeller. Under the action of the pressure difference between the suction and pressure surfaces of blades, some fluids form high-energy jets in the tip clearance area, known as tip leakage vortices (TLVs). TLV interacts with the flow of the main flow field, exerting a significant impact on the internal flow state, energy loss, and hydraulic performance of the pump. To identify the influence of TLVs on the internal flow field and energy loss of axial flow pumps, this work uses a modified partially averaged Navier–Stokes (PANS) model to perform full flow field numerical calculations for a certain axial flow pump and conducts a comparative analysis of the internal flow field energy dissipation, unsteady vortex structures, energy loss, and other characteristics under three different tip clearances: 0.2 mm (0.05%D), 0.6 mm (0.15%D), and 1.0 mm (0.25%D) based on the energy transport theory. The results indicate that at optimal operating conditions, the internal energy distribution of the fluid in each flow passage is uniform, and the energy loss is primarily caused by axial backflow in the tip area; under critical rotating stall conditions, clearance size affects the distribution state of enstrophy in the guide vane flow passage, leading to average enstrophy being highest at the rim area and the most uneven distribution of enstrophy, inducing larger energy loss in the impeller; during deep stall conditions, the unevenness of internal energy distribution is stronger than that under critical stall conditions, but the overall energy loss within the impeller flow area is lower than that under critical stall conditions, while energy unevenness is mitigated as the tip clearance size increases.

Research on Loss Characteristics Based on the Vibration Law of Granular Assembly

Particle damping technology is a typical passive vibration damping technology. In order to further explore the energy dissipation characteristics of particle dampers under different excitation, the relationship between internal vibration state and energy dissipation is analyzed. Based on the analysis of the motion state of granular assembly inside three‐dimensional cylindrical particles, the steady‐state energy flow method is used to study the loss characteristics of the granular assembly with different vibration laws. The research is carried out under the condition of excitation reduced acceleration of 0–8 and excitation frequency of 0–300 Hz. The results show that the loss capacity of the particles is enhanced when the vibration state of the particles changes from solid‐like to other motion states. At frequencies above 250 Hz, the particle microvibrational and intermediate‐vibrational loss effects are more significant. The loss capacity of the granular assembly shows frequency‐dependent characteristics and is affected by frequency and reduced acceleration. With the increase of the reduced acceleration, the loss capacity of particles is enhanced and shows a local peak effect as the frequency increases. The increase of the particle size enhances the loss ability in the microvibrational state and the intermediate‐vibrational state. By changing the vibrational state, the energy dissipation capacity of particle damper can be enhanced, which may provide a new idea for designing optimal granular dampers.

Internal shocks hydrodynamics: the collision of two cold shells in detail

ABSTRACT Emission in many astrophysical transients originates from a shocked fluid. A central engine typically produces an outflow with varying speeds, leading to internal collisions within the outflow at finite distances from the source. Each such collision produces a pair of forward and reverse shocks with the two shocked regions separated by a contact discontinuity (CD). As a useful approximation, we consider the head-on collision between two cold and uniform shells (a slower leading shell and a faster trailing shell) of finite radial width, and study the dynamics of shock propagation in planar geometry. We find significant differences between the forward and reverse shocks, in terms of their strength, internal energy production efficiency, and the time it takes for the shocks to sweep through the respective shells. We consider the subsequent propagation of rarefaction waves in the shocked regions and explore the cases where these waves can catch up with the shock fronts and thereby limit the internal energy dissipation. We demonstrate the importance of energy transfer from the trailing to leading shell through pdV work across the CD. We outline the parameter space regions relevant for models of different transients,e.g. Gamma-ray burst internal shock model, fast radio burst blast wave model, Giant flare due to magnetars, and superluminous supernovae ejecta. We find that the reverse shock likely dominates the internal energy production for many astrophysical transients.

Three-dimensional discretization-based kinematic analyses of prestressed anchor cables reinforced rotational slopes subjected to earthquakes

Prestressed anchor cables are commonly utilized to reinforce slopes in earthquake-prone zones. The existing upper bound limit analyses of seismic slopes reinforced with prestressed anchor cables have the following limitations: (1) neglecting variable seismic excitations; (2) ignoring the three-dimensional spatial layout of cables because of using the plane-strain analysis. In this study, the time-space effects of seismic waves are analytically described by sin-cos functions incorporating wave amplification or soil damping. Based on the upper bound of plastic theory and a three-dimensional discretized failure mechanism, internal energy dissipation rate and work rates contributed by gravitational forces, variable seismic excitations, and prestressed anchor cables are computed. An energy-based function of dynamic factors of safety (DFS) is established, followed by a global optimization to identify the critical harmonic pattern of DFS. The accuracy is checked by numerical simulations where the seismic stability of an engineering slope adjacent to Yu-Huai railway is evaluated. Comparisons also show that the conventional simplified method not only cannot reflect the spatial layout of cables but also overestimate the mechanical contribution of cables. Finally, the dominant effects of the layout of cables, soil properties as well as physical parameters of seismic waves on the DFS and the critical failure mechanism are discussed.

FED evaluation in a small double-suction reversible pump turbine considering sediment erosion

Double-suction pump-turbines are a special type of reversible pump-turbine which serves the pumped storage hydro power plant. Enhancing the energy conversion efficiency of the power station can be effectively achieved by reducing the internal Flow Energy Dissipation (FED) within the pump-turbine. The key to addressing this challenge lies in the identification of high FED regions and conducting visualized analyses. In this study, computational fluid dynamics (CFD), thermodynamic calculation methods and the Finnie erosion model are combined to perform two-phase flow numerical simulations of a specific double-suction pump-turbine model under both pump and turbine operating modes. We analyzed the FED in different regions off wall. The energy loss distribution is provided within these five regions for the volute casing, suction chamber, and impeller separately, and conducted an analysis of component wear. The research findings revealed that, in the pump mode, FED primarily concentrates within the volute casing, while in the turbine mode, it is concentrated within the suction chamber, with both regions accounting for over 70 % of the total energy dissipation. The proportion of internal FED in five regions at varying distances from the wall for each component showed significant disparities under different operating conditions, closely related to the internal flow characteristics of the components. In pump mode, wear primarily occurs in the volute casing, while the wear in the suction chamber and impeller can be considered negligible. In turbine mode, each component experiences some level of wear. This provides a foundation for reducing flow energy losses and preventing sediment erosion.

Emergence of precursor instabilities in geo-processes: Insights from dense active matter

We present the hypothesis that investigation of precursor mechanisms to large scale instabilities, that have so far been overlooked in geo-processes, is possible. These precursor processes are evident in multicomponent materials, such as granular matter, when driven far from equilibrium on its microscale. The material is then classified as “dense active matter” with unexpected behaviour by non-local dissipation of internal energy releasing its dynamic incompatibility with the macroscopic gradients as self-excitation waves under external forcing. These instabilities are known in solid mechanics as flutter instabilities, nucleating at what is more widely known as an “exceptional point” in a variety of systems when two or more eigenvalues of the system coalesce. The common principle to connect processes at and across their characteristic scales is investigated using a minimalist formulation by coupling the scalar field variables of solid and fluid pressures in a compacting porous medium. We present a multiphysics generalisation of the phenomenon to the exciting findings of fluctuations with oscillatory exponential growth which nucleate at the exceptional point for inception of complex conjugate eigenmodes and propose a rigorous theory based on the extension of Onsager's theorem to non-local processes. Future work will need to compare model predictions to carefully designed laboratory experiments and expand the work to bridge the scale of the laboratory to the scale of field applications including design of new sensors tuned for detecting exceptional points preceding collapse of materials.

Probabilistic assessment of seismic earth pressure against backfills with a nonlinear failure criterion

A novel approach for the probabilistic assessment of seismic earth pressure against nonlinear backfills is introduced in this study. To implement reliability-based design for the retaining structures under seismic loading condition, nonlinear upper bound analysis is adopted to obtain the seismic earth pressure through optimization procedure. Firstly, rigorous analytical function is formulated to reveal the normal-shear stress information along the failure surface in soil with nonlinear failure criterion. Subsequently, a kinematic equation is put forward to estimate the seismic earth pressures by balancing the external work rate and the internal energy dissipation rate. The solutions are verified by the Discontinuity Layout Optimization numerical modellings based on the derived stress data from the proposed method. To consider the probability analysis of nonlinear backfill properties, the moment method is presented by combining the adaptive dimension decomposition with the direct integral method. According to the estimated first four statistical moments, the approximated probability density function of the performance function is determined contently. Finally, the failure probability of seismic earth pressure is calculated based on the proposed moment method. Two numerical examples demonstrate that the moment method can be adapted to the characteristics of nonlinear backfills and further improve the accuracy of reliability estimation by introducing higher-order moments analytically.