Traditional casting preparation of Cu-Fe alloy is difficult, especially when Fe content is relatively high, because there is a metastable immiscible region of liquid components between copper (Cu) and iron (Fe), which causes serious compositional segregation in Cu-Fe alloys and leads to low strength and undesirable electrical conductivity of the alloys. In this study, Cu-50Fe alloy was fabricated by chemical co-precipitation and powder metallurgy. Cu-Fe mixed powders prepared by chemical co-precipitation have an average particle size of about 3.5 µm and a near-spherical shape. Copper and iron phases in the fabricated alloy intertwine with each other. After cold deformation, copper and iron phases are elongated along the cold deformation direction to form strips. During aging treatment, a number of Fe particles with diameter of 10–50 nm precipitate in Cu phases in the alloy. The tensile strength and electrical conductivity of the deformed and aged Cu-50Fe alloy are 651 MPa and 41.5%IACS, respectively.

2195 aluminum-lithium alloy has numerous applications in industrial production, and the different initial heat treatment state impacts its hot deformation behavior. Therefore, this work seeks to examine the impact of heat treatment states on the microstructure development and deformation behavior of 2195 Al-Li alloys. The experiments have been carried out on a Gleeble-3800 thermo-mechanical simulator in the temperature range 350–500 °C and with a strain rate of 0.01–10 s⁻¹. The microstructure analysis in various regions was compared, and constitutive models and processing maps of the alloys were produced. At high deformation temperatures (400–500 °), the peak stress of the T3 and T8 samples is nearly the same. Low angle boundaries (LABs) and the content of dynamic recrystallization have also been found. Due to solution strengthening and deformation strengthening effects, the 2195-T8 Al-Li alloy plate exhibited a larger deformation activation energy than the 2195-T3 Al-Li alloy. The hot working windows of the Al-Li alloys 2195-T3 and 2195-T8 were determined to be 475–500 ° and 0.01–0.1 s⁻¹, respectively. The research can serve as useful assistance for the Al-Li alloy’s ideal heat treatment conditions during hot working processing.

In this study, TiO_x<1 powders obtained from the combustion synthesis of TiO₂ and Mg was used as cathode to prepare low-oxygen titanium powders by electrochemical deoxidation process. The mechanism of oxygen removal, composition and morphology change of TiO_x<1 powders during electrode oxidation were investigated. The residual oxygen content in electrodeoxidized TiO_x<1 powders is linearly related to the deoxidation time. An obvious sintering neck between titanium particles with less than 0.35wt% oxygen could be observed after electrodeoxidation for 2 h. The removal of oxygen from Ti lattice promotes the surface diffusion of titanium atoms and leads to subsequent sintering and growth of TiO_x<1 powders in electrodeoxidation. The morphology of TiO_x<1 powders was transformed into coral and porous flakes from agglomerated small particles with a decrease in residual oxygen content and an extension of deoxidation time.

Electronic and optical properties of MAPbI₂Cl/RbPbI₃, MAPbI₂Cl/RbSnI₃ and MAPbI₃/RbSnI₂Cl heterostructures (MA=CH₃NH₃), were studied by first principle approach. Our calculations show that the MAPbI₃/RbSnI₂Cl and MAPbI₂Cl/RbSnI₃ structures have semiconductor properties with gaps of 0.19 and 0.97 eV, respectively. The effective masses calculations show that the MAPbI₂Cl/RbSnI₃ and MAPbI₃/RbSnI₂Cl can be used in photovoltaic devices. Also, the partial density of energy states (PDOS) diagrams show that in structure of MAPbI₃/RbSnI₂Cl, the two-dimensional electron gas is formed at the junction. In the following, by plotting the changes in the length of anion-cation bonds in the z direction and analyzing the local distribution of electrical potential surfaces, a ferroelectric-like behavior can be seen in the MAPbI₂Cl/RbSnI₃ and MAPbI₃/RbSnI₂Cl structures. Finally, in all cases, the reflectivity functions have large values and behave similar to shiny metals. Also, both MAPbI₂Cl/RbSnI₃ and MAPbI₃/RbSnI₂Cl heterostructures have absorption peaks in the visible range that are located at 412 and 701 nm, respectively.

Nominal compositions MgAl_2−x(Li_0.5Nb_0.5)_xO₄ (x=0–0.20) microwave dielectric ceramics were synthesized via the traditional solid-state reaction. The crystal structural characteristics, crystalline phases, and microwave dielectric properties were investigated. Rietveld refinement results showed that MgAl₂O₄ and Mg₅Nb₄O₁₅ form a stable two-phase system. Densification of the specimens decreases monotonically with the increase of (Li_0.5Nb_0.5)³⁺ content when sintered at 1550 °C. The variation tendency of quality factor (Q_f) is closely related to the densification, packing fraction and covalency. Likewise, the bond valence of the Al-site is responsible for the temperature coefficient of resonance frequency (τ_f). MgAl_2−x(Li_0.5Nb_0.5)_xO₄ ceramic with x=0.04 can be well densified by sintering at 1550 °C for 4 h and exhibits optimum microwave dielectric properties with ε_r=8.21, Q_f=81600 GHz, and τ_f=−94×10⁻⁶ °C⁻¹.

MgF₂ crystal windows for the weakness part of the optical system have obtained much attention due to the rapid development of photolithography and low-temperature silicon annealing. Investigating the mechanism of laser-induced damage on MgF₂ windows is much more important to push forward its optical applications, which has a few advantages, including lower light transmission, refractive index and higher hardness than CaF₂ crystals. In this work, the damage morphology induced by the 193 nm excimer laser under a threshold energy of 2.8 J/cm² shows obvious cracks and craters, which were observed by scanning electron microscopy (SEM). As the number and energy of laser pulses increase, damage to the rear surface increases exponentially. Interestingly, the rear surface of the window material was much more severely damaged than the front surface. Here, the electric field distribution of window material under 193 nm excimer laser irradiation was proposed to illustrate the damage physical mechanism, which is calculated by the 3D finite-difference time-domain (FDTD) method. In conclusion, the electric field intensity of the rear surface is stronger than that of the front surface due to defects in the window materials. Therefore, the improvement of optical crystal quality and optical geometry for the high power laser system could be considered to solve the damage problems for the application of MgF₂ optical windows.

In this study, direct ink writing (DIW) was applied to preparing polyvinylidene fluoride (PVDF) film. The rheological properties of inks were studied, and the influence of process parameters on material properties was systematically investigated by SEM, FTIR, DSC, dielectric, ferroelectric and piezoelectric properties testing. The results show that effective β-phase content of PVDF film prepared by printing parameters with printing needle size of 27G and printing speed of 20 mm/s was 52.38%, which was improved by 51.47% compared with the film prepared by solution casting. The high β-phase content improved the electrical properties of film. This is attributed to the orientation of PVDF molecular chains by the drawing force generated at printing needle and the shear force generated during extrusion. The piezoelectric output voltage increases approximately linearly with increasing finger height from the sensor. The sensitivity of the sensor is 78 mV/N, which is comparable to the performance of one prepared by solution casting and treated with electric polarization. The excellent piezoelectric performance of PVDF film demonstrates application potential in small deformation monitoring.

Nitrogen-doped (N-doped) graphene materials with highly-efficient and low cost have a promising application in fuel cell. Herein, N-doped 3D porous graphene catalyst (H-N-Gr) is successfully obtained by hydrothermal and high temperature pyrolysis. Graphitic carbon nitride (g-C₃N₄) and graphene can assemble intentionally into a stable composite precursor through hydrogen bonding and π-π conjugation in hydrothermal process, which can increase doping of nitrogen atoms without changing graphene structure after heat treatment. The prepared H-N-Gr has great catalytic activity for oxygen reduction reaction (ORR) due to its high specific surface area (470.3 m²/g) and the plenty of catalytically active pyridine nitrogen (25.4%) and graphitized nitrogen (37.3%) on the surface. In addition, the prepared H-N-Gr has better catalytic stability and methanol tolerance than commercial platinum-carbon catalysts, and exhibits high power density (202.90 mW/cm²) and rapid rate performance when assembled into zinc-air batteries. This research provides a simple and practical method to prepare a high performance ORR metal-free catalyst.

High-purity zirconium metal has been of rising significance to the nuclear and energy industry. However, zirconium exhibits a strong chemical affinity to oxygen, which causes high-purity zirconium metal to be difficult to produce cost-effectively. Powder metallurgy for preparing zirconium metal can achieve near net forming of zirconium metal. Zirconium powder can be prepared by deoxidation of zirconium hydride powder. In this study, an efficient process was proposed to prepare high-purity ZrH₂ using magnesium powder as reducing agent in hydrogen atmosphere. A specific investigation was conducted on the effect of hydrogen on the magnesiothermic reduction and deoxidation of ZrO₂. As indicated from the results, the oxygen content of the reduced powder in Ar was over three times that in H₂ atmosphere at 750 °C for 240 min. Moreover, a passive oxide layer, with a thickness of ~2.76 nm in H₂ and of ~8.51 nm in argon, was formed on the edge of the reduced powder. In accordance with thermodynamic calculation, hydrogen was found to be capable of destabilizing Zr-O solution. An ultra-high pure zirconium hydride powder containing <350×10⁻⁶ oxygen and particle size of <100 µm was prepared as assisted by hydrogen.

Pyrolysis is a promising technology to treat waste printed circuit boards (WPCBs) with significant advantages of full source utilization, high separation efficiency and scarce pollutant emissions. In this work, TG and DTG analyses were performed to determine pyrolysis characteristics. The kinetic analysis adopting the Starink Kissinger-Akahira-Sunose (SKAS) model was conducted to confirm the apparent activation energy (E_α). Pyrolysis products were collected using a lab-scale pyrolyzer. GC-MS analysis coupled with MS-DIAL data processing was applied to clarify the distribution pattern of valuable liquid products. The results indicated that the main thermal decomposition of WPCBs occurred within the temperature range of 157–664 °C, with E_α ranging from 80.70 to 279.46 kJ/mol. During pyrolysis, the WPCBs were converted into three kinds of products, in which solid and gas products could be applied in the field of materials and energy. The composition of WPCBs oil products was complicated and sensitive to the pyrolysis temperature. The largest proportion of valuable liquid products (82.94%) was obtained at 600 °C, containing 52.87% monocyclic aromatic phenols, 4.39% polycyclic aromatic phenols, 3.07% brominated phenols, and 22.61% hydrocarbons, respectively. These valuable liquid products would be an attractive alternative as raw materials for the synthesis of phenolic resins and the production of petrochemicals.

A process for recovering both Eu and Y from the discarded cathode ray tube (CRT) display was introduced. The developed process involved a directional transformation of waste CRT phosphors with concentrated sulfuric acid followed by leaching with water. Rare earth metal ions combined with sulfate to form rare earth sulfates and then were extracted by water leaching, while S²⁻ was oxidized to form sulfur, which was volatilized in gaseous form, thus avoiding the formation of the highly toxic gas H₂S. This study showed that in the optimized conditions, the ratio of concentrated sulfuric acid to sample was 8:5 mL/g and transformation time for 30 min under 85 °C, the liquid-to-solid ratio was 10:1 mL/g and leaching time was 30 min under 85 °C. The leaching solution with Y concentration of 8.26 g/L and Eu concentration of 0.57 g/L was obtained and the average leaching efficiencies of Y and Eu were 99.77% and 99.24%, respectively.

Due to many problems such as pipe blockage, environmental pollution, and the difficulty of recovering precious metals, caused by extensive use of lime, the conventional program using lime (CaO) as the inhibitor and xanthates (e. g., sodium butylxanthate) (BX) as the collector has become increasingly restricted in use, and lime-free flotation processes are increasingly advocated. In this study, a novel process with Z200 as the collector and pyrogallic acid (PGA) as the inhibitor was innovatively proposed and applied to separate copper-gold sulfide ore and pyrite in Hubei Province, China. In laboratory experiments, this new reagent system achieved a substantially better separation of copper-gold sulfide ore and pyrite than the conventional process program. First-principles calculations based on density functional theory (DFT) were used to understand the separation mechanism of the new reagent scheme. The DFT simulations showed that PGA had a much stronger depression effect on pyrite than chalcopyrite, whereas Z200 exhibited a stronger collecting ability for chalcopyrite than pyrite, which together explains the effectiveness of the new reagent system at the molecular level. This work sheds some new light on the potential of adopting new and eco-friendly reagent schemes in the utilization of mineral resources.

A novel surfactant dibutyl (2-(hydroxyamino)-2-oxoethyl) phosphonate (DBPHA) was designed and synthesized as a cassiterite flotation collector. Micro-flotation experiment results indicated that under the condition of pH~9.00, collector initial concentration 8×10⁻⁵ mol/L, the flotation recovery of cassiterite reached about 90% using DBPHA as collector, while only 22% using BHA as collector. The adsorption mechanism of DBPHA on the cassiterite surface was investigated by zeta potential, Fourier transform infrared spectroscopy, X-ray photoelectron spectroscopy measurements and density functional theory calculations. The changes in the zeta potential for the DBPHA-treated cassiterite particles demonstrated that DBPHA chemisorbed onto the cassiterite surface, while the addition of benzohydroxamic acid (BHA) barely changed the zeta potential of cassiterite. Density functional theory predicted that DBPHA possessed two active sites of the reaction center, namely, hydroxamate and phosphoryl groups, while BHA only had one hydroxamate group. Fourier transform infrared spectroscopy and high-resolution X-ray photoelectron spectroscopy spectra revealed that the chemisorption of DBPHA on cassiterite produced DBPHA-Sn surface species, where both hydroxamate (—C(=O) —NHOH) and phosphoryl (P=O) groups bonded with surface Sn atoms, causing the hydrophobic groups of DBPHA to orient towards the solutions for attaching bubbles. Therefore, an effective enrichment of cassiterite was achieved.

This paper demonstrates the impact of chemical reactions on the onset of thermal convection in micropolar nanofluid using no flux and rough boundaries. For solving rough boundaries, we have implemented a Saffman-interface condition. Here, we consider the micropolar non-Newtonian nanofluid, which has an important role in many industrial applications. For linear stability, we use the normal mode technique (NMT) to convert the controlling system of a partial differential equation (PDE) into an eigenvalue problem (EVP) and solve it numerically using the finite difference based three stage Lobatto IIIa method. The stationary mode is found to be the dominant mode of convection. Increasing the values of coupling coefficient between heat flux and spin Hall effect (δ), the coupling coefficient between spin Hall effects and vorticity (K), roughness parameters (λ₁, λ₂), chemical reaction parameter (Cr) and modified diffusivity ratio (N_A) and parameter of micro-polarity (A) in the nanofluid delays the convection, thus stabilizing the system. Later, with 81 data points, an artificial neural network (ANN) embedded with multiplayer perception (MLP) is used to determine the relationship between four controlling parameters and Rayleigh critical number.

An accurate power curve is essential for monitoring the wind turbine because this curve can reflect the operating condition of the equipment. However, some newly installed wind turbines may not have enough training data to fit an accurate power curve and lead to poor monitoring results. In this work, considering the insufficient data, we proposed a data expansion based on piecewise regression strategy to monitor the wind turbine with an incremental monitoring strategy. The proposed method can be divided into the offline modeling stage and the online monitoring stage. During offline modeling, a novel mapping function was first designed to expand the insufficient data by mapping the data of other data sets onto the insufficient target data set. In this way, there will be enough training data for the target wind turbine. Then, a piecewise modeling strategy was designed to condense the information of the expanded data into a small number of samples and then fit the power curve. Based on this strategy, the power curve can be accurately fitted with low computational complexity. During online monitoring, the power was predicted by the power curve, and finally, the operating condition can be monitored by comparing the prediction with the observed power. Meanwhile, an incremental learning strategy was proposed to improve both the prediction and monitoring accuracy by updating the power curve model using the newly arrived data. A real case in the experiment illustrated that the proposed monitoring method can accurately detect abnormal behavior with 92.77% detection accuracy while facing insufficient data.

The creep characteristics of coal pillars left over from old mining directly affect the long-term stability of underground engineering. To study the creep characteristics and long-term stability of the No. 3 anthracite pillar in Qinshui Coal Field, Shanxi Province, China, conventional triaxial compression and triaxial creep tests were conducted under four low confining pressures (0.5, 1.0, 1.5 and 2.0 MPa), and the creep laws of the anthracite samples under different confining pressures were explored. Moreover, based on the test data, a nonlinear viscoelastic-plastic creep model was established which could better describe each creep stage. The test results show that: 1) when the axial stress is higher than the yield stress, the creep of anthracite undergoes three stages: initial creep, steady creep, and accelerated creep; 2) the instantaneous elastic strain of anthracite increases linearly with the axial stress level, and the smaller the confining pressure was, the faster the instantaneous elastic strain increased; 3) Compared with the instantaneous strength, the long-term strength of anthracite decreased by approximately 20%. The creep properties reduced the shear strength of anthracite, and compared with the short-term shear strength, the internal friction angle and cohesion decreased by 8% and 14%, respectively.

In deep coal mining, complex stress and mining conditions often cause large deformation and roof falling of roadway, which seriously threatens the production safety of coal mines. This study investigated the stress characteristics, failure mechanism, and control methods of gob-side roadway (GSR) at Hongqinghe Coal Mine in the Xinjie deep mining area, Inner Mongolia, China. The long and short arm F-shaped roof structure models during the different mining stages for the first working face were established. The stress calculation methods for GSR surrounding rock were proposed based on foundation static load (FSL), mining-induced additional static load (MIASL), and disturbance dynamic load (DDL). Moreover, the stability of GSR was analyzed. The failure mechanism of GSR was revealed. It was concluded that the GSR failure may occur due to the high stress and energy induced by the additive effects of the FSL, the MIASL, and the DDL. The coal pillar width of 5–10 m can provide a low stress environment for GSR, conducive to reducing the risk of GSR failure. The suitable control methods for GSR were proposed, which included selecting reasonable coal pillar widths, cutting off the dynamic load sources, reducing the static load stress concentration, and application of energy-absorbing bolts. The findings may provide valuable insights for controlling roadway surrounding rock in similar conditions.

Hydraulic conductivity is a vital parameter that affects the mechanical stability of cemented tailings backfill (CTB) after placement into underground stope. Triaxial seepage tests were conducted on the CTB samples to investigate the effects of the cement content (2%, 3% and 5%), curing age (3, 7 and 28 d) and confining pressure (100, 200, 300 and 400 kPa) on the evolution of hydraulic conductivity. In addition, the change of hydraulic conductivity with axial strain during triaxial compression was revealed as well. The results show that the static hydraulic conductivity of CTBs shows a non-linear decrease with increasing of curing age length and cement content, and the confining pressure plays a negative effect on the static hydraulic conductivity. The dynamic hydraulic conductivity is closely associated with the deformation of CTB during the triaxial compression. The hydraulic conductivity of CTB shows a decrease firstly, but increases with further increase in the axial strain. The volumetric strain curves show volume shrinkage at first and subsequently expansion, which can be used to explain the dynamic hydraulic conductivity evolution under triaxial compression. The results can provide guide reference for backfill strength and drainage design.

To explore bearing characteristics of hydraulic support groups in shallow-buried thin bedrock ultra-long working faces, a beam-on-elastic foundation (BEF) mechanical model was established for the coal walls, supports, and roof of the working face. The influence of seven factors on the resistance of the supports was investigated. The theoretical calculation and the actual measurement are in good agreement. Results show that working resistance of supports is distributed in two patterns: single-peak and M-shaped three-peak forms. The working face length and main roof thickness and elastic modulus have influence on the shape of the resistance distribution curve and the range of high support resistance. The mining height and overlying strata load affect the value of the curve. The support stiffness affects the range of high resistance. The roadway sidewalls stiffness affects the support resistance near the roadway side. Based on this, key safety control measures for shallow ultra-long working faces with thin bedrocks including determination of appropriate working face length, zonal regulation of supports, cooperative control of coal walls, and active reinforcement of roadway sidewalls were proposed. The research results provide a theoretical basis for design of support resistance and disaster prevention in shallow ultra-long working faces with thin bedrock.

This paper proposes an analytical model for the longitudinal deformation response of cross-fault shield tunnels, in which the tunnel is assumed to be a Timoshenko beam placed on Winkler’s foundation. The plastic deformation behavior of circumferential joints and the influence of horizontal foundation friction are considered in the proposed model. A case study of normal faulting based on convincing numerical simulations is carried out to verify the rationality of the proposed model. Subsequently, the plastic deformation characteristics and distribution of circumferential joints are analyzed, and the factors affecting the longitudinal response of the tunnel are discussed through parametric analysis. The analysis results demonstrate that the proposed analytical model is reliable and applicable to calculating the longitudinal response of cross-fault shield tunnel, especially in evaluating the deformation of the circumferential joints under normal faulting. Severe plastic deformation is observed on the annular joints when the shield tunnel is subjected to 10 cm faulting. Under crossing active fault, the ground has a more significant restriction on the longitudinal deformation of the shield tunnel, resulting in a larger deformation of circumferential joints. A larger elastic modulus of the ground leads to a more notable longitudinal deformation of the tunnel lining. When the width of the fault fracture zone is not considered, the results of longitudinal internal force and deformation of shield tunnels are conservative. In the plastic deformation stage of the circumferential joints, the larger the plastic equivalent bending stiffness ratio of the shield tunnel, the slighter the plastic deformation of circumferential joints. The proposed analytical solution can be used to predict the joint deformation of cross-fault shield tunnels and provide guidance for the waterproof design of shield tunnels.

Rockburst hazards caused by excavation in deep tunnel boring machine (TBM) tunnels endanger construction safety. Based on 43 rockburst events and related microseismic (MS) energies in the deep TBM tunnels in the Neelum-Jhelum hydropower station in Pakistan, the MS energy characteristics and intensity identification of rockburst events in deep TBM tunnels were studied. The rockburst event was preprocossed using distance discrimination method for case expansion, and the characteristics of MS energies of rockburst events with different intensities and lithological conditions in TBM tunnel were investigated. Using the quantitative parameter of MS energy, a criterion for identifying the rockburst intensity in deep TBM tunnels under different conditions was established. The higher the rockburst intensity, the greater the quantitative threshold of MS energy, and the two show a nonlinear relationship. The threshold value of MS energy for sandstone is greater than that of siltstone for the same intensity of rockburst. It is necessary to differentiate the lithology when identifying the intensity of rockburst events. The established criterion was validated in the project, and the results show that the established criterion is reliable. The results can provide a basis for understanding rockburst events and provide advance warning thereof in deep TBM tunnels.

The time-frequency analysis method based on Hilbert-Huang transform is proposed and used to the seismic response analysis of accumulation landslide reinforced by pile-plate retaining wall. Taking the landslide along the Chengdu-Lanzhou Railway as the prototype, the shaking table test of the accumulation landslide reinforced by pile-plate retaining wall with a physical dimension similarity ratio of 1: 10 is designed and carried out. The results show that the acceleration response of the accumulation landslide shows obvious elevation effect in the process of loading different amplitude seismic waves, and the elevation effect of the landslide is the most significant under the 0.3g seismic wave. Then the elevation effect decreases with the increase of seismic wave amplitude. The dynamic earth pressure of the pile is distributed nonlinearly along the pile body, and the size and range of its envelope are directly proportional to the seismic wave amplitude. The maximum dynamic earth pressure of the pile appears at the embedded section, so attention should be paid to the reinforcement design of this part. The displacement response of pile also increases gradually with the seismic amplitude, and the coupling displacement mode changes from translation to rotation. In addition, it is feasible to use the time-frequency analysis method based on HHT transform to study the seismic stability of accumulation landslide reinforced by pile-plate retaining wall. The Hilbert energy spectrum analysis shows that the seismic energy is mainly concentrated in time domain of 2–6 s, and the corresponding frequency domain is 10–50 Hz. With the increase of input seismic amplitude, the difference of Hilbert energy between sliding bed and sliding body measurement points in time-frequency domain increases, and the difference of seismic response between them increases significantly. The damage inside the landslide can be identified by Hilbert marginal spectrum. Under the action of pile plate retaining wall, the damage at the bottom of the landslide mainly occurs on the slope, while the damage in the middle of the landslide mainly occurs inside.

In this paper, an efficient computation method based on a multi-GPU parallel algorithm is proposed to overcome the low efficiency in random calculation of the train-track-soil coupled system (TTSCS). Firstly, for the large time consumption caused by solving multiple independent equations of TTSCS at different frequency points in serially random vibration analysis, the multi-GPU parallel algorithm is proposed and programmed based on the OpenMP-CUDA algorithm. The tasks of solving multiple linear equations for random vibration analysis of the TTSCS are distributed to different GPUs for parallel execution. On each GPU, the large sparse linear equations of TTSCS are solved by the CUDA-based parallel preconditioned conjugate gradient (PCG) method, and the large sparse matrix is stored in the compressed sparse row (CSR) format to save memory space. Then, the parallel computing program is implemented on the MATLAB-CUDA hybrid platform. Finally, numerical examples show that the efficiency of solving large sparse linear equations based on the multi-GPU parallel algorithm implemented on a 4-GPU node and the GPU-accelerated PCG algorithm implemented on a personal computer with a single GPU is 22.59 times and 3.75 times that of the multi-point synchronization algorithm (MPSA), respectively.

The deformation behavior of subgrade soil is crucial to the design of subgrade structures and to maintaining the long-term performance of pavements. Resilient modulus (MR) and permanent deformation (PD) are important indices to characterize elastic deformation and plastic deformation of subgrade soils, respectively. This study aims to investigate the evaluation of deformation behavior (MR and PD) of subgrade clay under deviatoric stress, confining pressure, moisture content, loading cycles, and freeze-thaw (FT) cycles by repeated triaxial load test. An evolution model for calculating PD was proposed based on experimental data. The results showed that the influence of FT cycles on MR and PD was obvious. The largest damage and stable trend were in the first and sixth FT cycles, respectively. MR decreases and PD increases rapidly during the first 2000 loading cycles. The PD evolution model consisting of deviator stress, confining pressure, moisture content, loading cycles and FT cycles of explicit modification functions was proposed and validated. The results obtained in this study contribute to a better understanding of the deformation behavior of subgrade clay under FT cycles.