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Huang Kaixuan, Ding Zhe, Zhang Yan, Li Xiaobai
With the rapid development of additive manufacturing technology, lattice structures have attracted extensive attention due to their excellent mechanical properties, such as high specific strength and high specific stiffness. However, the designs of lattice structures are mostly based on the assumption of uniform distribution, resulting in a relatively poor load-bearing capacity. This paper proposes a layer-wise graded lattice structure design method based on a topology optimization technology. Firstly, an explicit description model of lattice geometric configuration is established by using the level set function, and a shape interpolation technology is employed to generate the graded configurations of lattice cells. Secondly, a prediction model of macro effective mechanical property for these graded lattice cells is constructed based on the Kriging metamodel, achieving the essential relationship between the effective density of macro element and the effective mechanical property of micro lattice cell. Then, with the maximum stiffness of lattice structures as the optimization objective, the allowable material usage amount and structural system equilibrium equation as the constraint conditions, a layer-wise graded topology optimization model of lattice structures is established, which is solved numerically by using the OC algorithm. The numerical results indicate that the proposed method can realize the optimal layer-wise graded design of lattice structures, which not only fully improve the load bearing performance of lattice structures, but also ensure the geometric connectivity between different graded lattice cells. Finally, the quasi-static compression simulation analyses of the layer-wise graded lattice structures, the traditional uniform lattice structures and the linear graded lattice structures are carried out and discussed. The simulation results show that, compared with the traditional uniform lattice structures and the linear graded lattice structures, the loading capacity of the layer-wise graded lattice structures is significantly improved. The proposed method provides a theoretical reference for the design of high loading lattice structures.
, Available online  , doi: 10.6052/0459-1879-22-363
Shen Guozhe, Wang Ruiyang, Xia Yang, Zheng Guojun
Thin plate structures are widely used in the fields of automobiles, ships, and aerospace because of their excellent load-bearing performance, light weight and easy processing. However, in practical applications, thin plate structures often produce large displacement, rotation and even cause crack initiation and growth under small loads, and then the overall structure fractures. Therefore, it is of great engineering practical significance to establish a crack growth and fracture simulation model of thin plate structures in the process of large deformation. In this paper, a peridynamic (PD) and classical continuum mechanics (CCM) coupling model for geometrically nonlinear deformation and fracture analysis of thin plate structures is established. First of all, the updated Lagrangian formula is used to obtain the expression of virtual strain energy density increment of thin plates at each increment step in large deformation analysis under von Karman's hypothesis. Then, the PD constitutive parameters of geometrically nonlinear micro-beam bond are obtained by using the virtual work principle and homogenization hypothesis. After that, the virtual strain energy density increments of the PD model and CCM model for geometrically large deformation thin plate were respectively established, and the geometrically large deformation PD-CCM coupling model of the thin plate was established. Finally, the progressive fracture process of the thin plate structure under the action of lateral deformation is simulated, and the simulation results are highly consistent with the experimental results, which verifies the accuracy of the proposed geometrically nonlinear PD-CCM coupling model. It is shown that the proposed geometrically nonlinear PD-CCM coupling model is simple and efficient without restriction on material parameters and consideration of boundary effects, and can be well used to predict local damage and structural fracture of thin plate structures during geometrically large deformations. It is beneficial to the fracture safety evaluation and theoretical development of thin plate structures.
, Available online  , doi: 10.6052/0459-1879-22-519
Ji Ziqing, Bai Yuchuan, Xu Haijue
In the hydrodynamic and processing research of meandering river, it is implicitly assumed that the relationship between secondary flow and secondary turbulence is the same as that between mean flow and turbulence in open channel flows. However, there is no relevant turbulence research to support this implicit assumption, due to the limitation of DNS model and PIV measurement at high Reynolds number. The differences and similarities research of turbulent structures development between meandering channel and straight channel flow are benefit to the secondary turbulent flow in meandering rivers. A planar two-dimensional NS equation in orthogonal coordinate system and the two-parameter perturbation method were established to solve the weak nonlinear laminar flow and flow instability problem in the meandering channel. And a governing equation, named with Extended Orr-Sommerfeld equation (EOS equation) was derived to solve the eigenvalue problem of planer flow with meandering boundary. The weak nonlinear laminar flow is combination of a series of meandering harmonic components, in which the linear component causes the velocity difference between the two walls, and the nonlinear component increases exponentially with the increase of Reynolds number. The first modal of the disturbance growth rate spectrum is similar to that of the straight channel flow, which is composed of three type curves and divided four disturbance wave bands. However, the disturbance flow field at the longwave band and the shortwave band is different from that of the straight flow. Specially, the velocity disturbance at shortwave band is similar to that of the Kelvin - Helmholtz vortex, may due to the velocity difference caused by linear component of laminar. The two meandering parameters have a certain selectivity to the internal disturbance in channel. The larger the angular amplitude is, the faster the disturbance grows. With the increase of the meandering wavenumber, the disturbance growth rate increases at first and then decreases. The disturbed flow field is formed by superposition of a typical TS wave and a pair of wave packets. The wave packet pair has only longitudinal velocity components, with two envelopes controlled by the boundary wavenumber and interior TS wave with the same parameters as TS wave in the wave packet.
, Available online  , doi: 10.6052/0459-1879-22-570
Li Kai, Yang Jingyuan, Gao Chuanqiang, Ye Kun, Zhang Weiwei
The static aeroelastic problem is concerned with those physical phenomena which involve significant mutual interaction between elastic and aerodynamic forces, which has dramatical influence on the overall flight performance and security of the aircraft. The computational fluid dynamics (CFD) and computational structural dynamics (CSD) coupling method is an essential and accurate tool to account for the impact of static aeroelastic problems in the design of the advanced aircraft. However, aerodynamic loads based on CFD simulation require a large computational cost and time, which can’t meet the need of the design stage. Therefore, many aerodynamic reduced order models based on CFD have been proposed in order to maintain a balance between the computational accuracy and efficiency. Then, an efficient and accurate steady aerodynamic reduced order model for the static aeroelastic analysis is developed in this work, using proper orthogonal decomposition (POD) and Kriging surrogate model to replace the CFD simulations and couple the finite element analysis (FEA). Compared with the conventional static aeroelastic analysis with the modal method, the proposed approach can deal with more complex static aeroelastic problems and predict the aerodynamic distribution loads in the static aeroelastic deformation. Then, the performance of the proposed approach is evaluated by a transonic flow with multiple Mach numbers and angles of attack past a three dimensional HIRENASD wing configuration, which is initiated by Aachen University's Department of Mechanics to provide a benchmark test case for computational aeroelastic code validation. Results demonstrate that the relative error for the static displacement at the wing tip (Y/b = 0.99) of the CFD/CSD coupling method and the proposed approach is within 5%. In addition, the error for predicting aerodynamic distribution loads in the position of static equilibrium is within 5% and the computational efficiency is improved by the proposed approach at least 6 times for the static aeroelastic analysis.
, Available online  , doi: 10.6052/0459-1879-22-523
Shang Jiahao, Hu Guotun, Wang Qiu, Wang Yejun, Zhang Kun, Xiang Gaoxiang, Zhao Wei, Wei Bingchen
By taking advantages of rapid heat release, high specific impulse and simple combustion chamber structure, oblique detonation plays an important role in hypersonic air-breathing propulsion systems, which has been attracted more attentions in recent decades. However, due to the existence of technical difficulties, such as high-speed test environment generating, fuel and oxidant mixing, and high-temperature combustion flow-field structure measurement, the ground experimental research about oblique detonation wave at home and abroad is still limited at present. Thus, it’s difficult to support the development of oblique detonation engines. To study the wave structures and dynamic characteristics of the self-sustained propagating oblique detonation wave, investigation on oblique detonation induced by a hypersonic projectile launching has been conducted based on a two-stage light-gas gun device. The spherical projectile with a diameter of 30 mm is launched into a test chamber, in which fills with stoichiometric hydrogen/oxygen combustible mixture to induce the initiation of the detonation wave. In this work, two different shadowgraph techniques have been employed to record the structures of shock induced by the projectile. Three kinds of shock structures have been observed with different projectile velocities and filling pressure: shock induced combustion, detonation wave initiated by the projectile and steady oblique detonation wave around the projectile. A decrease in the filling pressure results in increasing length of transverse wave and unsteady flow structure of detonation wave. The measured oblique detonation wave angle agrees well with the theoretical result. The discrepancy of the shock wave angle between experiment and theory exists due to large angle of attack of the projectile, which is caused by aerodynamic instability. The propagation velocity of the oblique detonation wave is determined by oblique detonation wave angle at various points of detonation wave. Moreover, it shows that the detonation propagation velocity decays to the CJ detonation velocity as moving away from the projectile, and thus accelerate the attenuation of propagation velocity of the oblique detonation wave.
, Available online  , doi: 10.6052/0459-1879-22-536
Huang Ke, Zhang Jiaying, Wang Qingyun
In order to improve the flight performance of the aircraft, morphing technologies are used to change aerodynamic characteristics through smooth and continuous structural deformation. Since this new concept requires changing the structural shape to obtain the best performance, its inherent dynamic characteristics will be affected and even change its aeroelastic performance. In this paper, an equivalent modelling method of the two-dimensional flexible wing with camber morphing is developed. The dynamic model of the flexible wing is established based on the hypothesis of a non-uniform beam model. The analytical solution and natural frequencies are obtained by the method of Frobenius and verified by comparison with the finite element method solution. The errors of the first four natural frequencies are within 1% and the corresponding modes are consistent. The flexible wing is prepared by 3D printing engineering plastic (ABS) and silicone rubber skin. The Young's modulus of the 3D printing material and silicone rubber are respectively measured by dynamic measurement method and tensile test. The vibration response test platform is built to carry out vibration test of the flexible wing. It is found that the fundamental frequency obtained by vibration test is consistent with the theoretical model results, and the error is less than 3% compared with the finite element method. The equivalent modelling method of a two-dimensional flexible wing is established through theoretical analysis and experimental verification. The research results will provide theoretical support for applying the flexible trailing edge structures.
, Available online  , doi: 10.6052/0459-1879-22-551
Lu Ziyin, Zhang Xiaoyuan, Li Jinping, Ma Hu
As a special high-power pulse supply, magnetohydrodynamic(MHD) power generation device has many advantages, such as high efficiency, large capacity, and fast startup. The key to restrict the development of it is how to obtain the working gas with high conductivity. The driving capacity of detonation-driven is far beyond the conventional mode. It has unique advantages in providing high temperature and high conductivity gas. Applying the detonation-driven shock tube technology to MHD power generation is beneficial to breaking through the technical bottleneck, so an experimental study of inert gas MHD power generation based on detonation-driven shock tube was carried out. According to different ignition positions, detonation-driven shock tube can be divided into backward mode and forward mode. Backward detonation-driven mode can provide a long time and stable state of the gas, while forward detonation-driven mode has the advantage of producing high enthalpy gas. The test system is composed of detonation-driven shock tube, Laval nozzle, power channel, electromagnet, vacuum tank, load resistance and other measuring devices. In the test, plasma flow is generated by backward or forward detonation-driven shock tube. The inert gas is compressed to high temperature and high conductivity by shock wave, ionized into conductive plasma. The plasma accelerates to high speed inside the nozzle, then cut the magnetic induction line in linear shaped faraday-type generator to generate electricity. Under the condition of 0.9 T magnetic induction intensity, the stable output power at 3.5 Ω load reaches 1.9 kW by backward detonation-driven with a duration of 1.5 ms. With an external load of 0.035 Ω, the generator can produce up to 212 kW for a short time within 0.3 ms by forward detonation-driven, and the power density is 0.2 GW/m3. The experiment successfully verified the feasibility of inert gas MHD power generation by detonation-driven shock tube. And it provides a new method for the application and development of high-power pulse supply.
, Available online  , doi: 10.6052/0459-1879-22-576
Wang Haopeng, Yuan Xianxu, Chen Xi, Liu Shuyi, Lai Jiang, Liu Xiaodong
Transition from laminar to turbulent flow of the hypersonic boundary layer can increase the wall friction coefficient and heat conduction coefficient by 3 ~ 5 times, which has a significant influence on flight performance and safety of hypersonic vehicles. Wavy roughness is a possible passive control method to delay hypersonic boundary layer transition, and is thus of engineering significance. In this paper we investigate the effort of finite-length wavy roughnesses with different locations and heights on the stability of a Mach 6.5 flat-plate boundary layer using direct numerical simulation and linear stability theory (LST). DNS is employed to obtain the laminar base flow, and to study the linear evolution of fixed-frequency disturbances parametrically introduced upstream by blowing and suction. The effects of the relative position of the fast/slow mode synchronization point and the wavy roughness are revealed. It is found that when the wavy roughness is placed upstream of a disturbance’s synchronization point, the disturbance is damped compared to the smooth surface case; when the disturbance’s synchronization point is within or slightly downstream of the wavy roughness, the disturbance is generally enhanced. The effects of heights of wavy roughnesses are also considered. For the wavy roughness with small heights compared to the boundary layer thickness, the effect of wavy roughness is positively correlated with the height of the wavy roughness, while the effect is weakened by the higher wavy roughness. Linear stability theory can predict well the effects of wavy roughness on high-frequency disturbances, but exhibits large discrepancies with DNS in predicting the behaviors of moderate and low-frequency disturbances. This indicates that the receptivity process and the strong non-parallel effect in the vicinity of the wavy roughness neglected by LST should play an important role.
, Available online  , doi: 10.6052/0459-1879-22-327
Wei Zhigang, Chen Haibo, Luo Zhonglong, Hu Wenfeng
One of the biggest challenges for soft materials is to establish statistical mechanical models to correctly describe the relationship between its microstructure and macroscopic mechanical properties, and the statistical models for rubber-like materials still have some imperfections. Based on the macroscopically isotropic, continuous uniform and incompressible properties of rubber-like materials, combined with a non-Gaussian statistical model for molecular chains, a new elastic model for rubber material is proposed. The force transfer path between the corresponding points on the representative volume element is described by a subnetwork constrained to a region as a spiral helical tube, whose surfaces all deform affinely with the macroscopic deformation. The sub-network consists of molecular chains or chain segments linked end-to-end with random orientation and length. Hence, the constitutive model describing the macroscopic mechanical characteristics of the material is derived from the entropy of the subnetwork. A large number of test data were used to fit the constitutive model, which show that the model has very good accuracy. Especially, the proposed model with two parameters show very high reliability that it gives good predictions of the three basic test with the parameters derived from data-fitting with uniaxial tension data only. With the proposed curved affine tube confinement, this model can explain the incompressible properties of the material from the microstructure scale, overcome the shortcoming of straight tube model, and build a new model for the correlation between the stochastic at the micro scale and the uniform at the macro scale.
, Available online  , doi: 10.6052/0459-1879-22-435
Li Liping, Yu Honghao, Zhang Haitao, Pan Yishan
The ultra-low friction impact ground pressure of deep coal rock is essentially a time-varying process in which a large amount of coal rock mass is instable and sliding along the coal-rock interface, during which the friction and friction coefficient of the coal-rock interface change with time, and at the same time, the energy conversion characteristics of releasing energy from the impact kinetic energy of the coal-rock interfacial with the frictional force of the coal-rock interface. In order to quantitatively describe the energy conversion law of coal rock interface, the dimensional analysis method is introduced, and the elastic coefficient, damping coefficient and pending coefficient of coal rock are experimentally determined, and the expression of the friction coefficient of deep coal rock interface is given. Taking Shenyang Hongyang Three Mines as the research object, through the combination of experimental research and engineering practice, a new index of impact kinetic energy conversion rate is defined, the reliability of the built model is verified, and the law of coal-rock interface friction work to coal-rock impact kinetic energy conversion is quantitatively described. The results show that the interfacial friction coefficient of deep coal rocks decreases linearly with the increase of the amplitude of the impact load, and increases linearly with the increase of the frequency of the impact load. When the impact load amplitude is 5000 N and the impact load frequency is 500 Hz, the ultra-low friction effect occurs when the friction force of deep coal rock interface decreases by 97% and the reduction rate is 38.9 kN/ms ~ 41.38 kN/ms. For the first time, the ultra-low friction effect is quantitatively described in terms of friction reduction amplitude and reduction rate. Combined with the experimental and engineering actual analysis, it is found that the average experimental result of the energy consumption ratio is 0.441, and the calculation result of the "11.11" impact ground pressure of Hongyang Three Mines is 0.488, which is relatively close, which further proves the rationality of the proposed model.
, Available online  , doi: 10.6052/0459-1879-22-467
Zhang Yunfa, Kong Xianren
Nonlinear energy sink is a kind of vibration energy absorption device, which plays an important role in vibration suppression of structure. In this paper, the correlation analysis of vibration suppression for a system with combined nonlinear damping nonlinear energy sink is carried out. Firstly, the theoretical model of the system with combined nonlinear damping nonlinear energy sink is described. The motion equations of the system model are derived by using the complex variable average method, and the slow variable equations of the system are obtained. Secondly, the slow variable equations of the system are analyzed by using the multi-scale method. By studying the slow invariant manifold and phase trajectories of the system, the condition basis of the strongly modulated response of the system is described. In addition, the influence law of the external excitation amplitude on the frequency detuning coefficient interval in the presence of the strongly modulated response is revealed by analyzing the system with one-dimensional mapping. Finally, the energy spectrum, time response and Poincare mapping are applied to study the vibration suppression of the system with combined nonlinear damping nonlinear energy sink, the influence law of different damping ratio, damping and stiffness of nonlinear energy sink on its vibration suppression effect is revealed. Meanwhile, it is found that the response of the nonlinear energy sink with combined nonlinear damping is consistent with that of the main structure. In addition, it is verified that the nonlinear energy sink with combined nonlinear damping proposed in this study has good vibration suppression ability.
, Available online  , doi: 10.6052/0459-1879-22-563
Shen Nao, Li Xiaochun, Wang Lei
Seismic activity caused by fluid injection in sandstone reservoirs has been associated with the frictional properties of embedded faults or fractures. In order to study the frictional characteristics of fluid-bearing sandstone fractures under different temperature conditions, velocity stepping tests were carried out at varying temperature and pressure conditions (a temperature range of 25 °C ~ 140 °C and an effective normal stress range of 4 ~ 12 MPa) on dry, water saturated and CO2 injected sandstone fractures (obtained by saw cutting), respectively. The experimental results show that: (1) For dry sandstone fractures, increasing effective normal stress and increasing temperature can both increase the initial friction coefficient of fractures, while varying effective normal stress has no obvious effect on the frictional stability of fractures. An increase in temperature is found to enhance the frictional stability of fractures. (2) For sandstone fractures saturated by water, the initial friction coefficients of fractures also increase with the effective normal stresses, but they can be weakened by the rising temperatures, and increasing effective normal stress and temperature can both favor the frictional instability of fractures; (3) For the CO2 injected sandstone fractures, the initial friction coefficients of fractures are affected by the change in effective normal stress and temperature, which is opposite to that of water-saturated sandstone fractures. The frictional stability of fractures is affected by the ambient temperature, seemingly independent of the effective normal stress. To sum up, these experimental results suggest that the frictional characteristics of sandstone fractures are jointly controlled by the effective normal stress, temperature and the injected fluid type. These experimental results may provide a better understanding of earthquakes induced by fluid injection.
, Available online  , doi: 10.6052/0459-1879-22-400
Liu Xiaohua, Zhang Tao, Liu Xiaochen, Jiang Yi
The building sector is a key sector to achieve the double carbon target, and under the guidance of the double carbon target, the building energy system needs to make innovation. Therefore, the development tasks of building energy system are discussed in depth in this paper, and the development direction of building energy system facing the dual carbon target is proposed. The traditional building energy system is mainly to meet the basic energy needs of the building itself, such as cold, heat and electricity. Under the dual carbon target, there needs to be a shift from energy efficient buildings to new targets for low-carbon buildings. The building energy system needs to make changes in reducing the energy demand of the building body, fully electrifying the building energy system, improving the energy efficiency level of the building energy system, realizing flexible adjustment and becoming an adjustable load of the energy system with flexible adjustment ability. It needs to shift from being a simple consumer of energy systems to a complex that integrates energy production, consumption, regulation and storage. To build low carbon building energy system as the goal, the trend of research of building energy systems is discussed: the need to further meet the demand of the building energy to make a full understanding of the building energy requirements, e.g. the energy requirements for building thermal environment is a key section for building energy consumption and energy conservation, need further integration architecture and traffic, electricity and other fields, from the monomer building to multiple scales, such as architecture, urban construction as the carrier to build new energy system between urban and rural areas. The current research provides a useful reference for building energy system to realize its own role transformation and accelerate the realization of energy system reform under the dual carbon target.
, Available online  , doi: 10.6052/0459-1879-22-462
Zhang Shengting, Li Jing, Chen Zhangxing, Zhang Tao, Wu Keliu, Feng Dong, Bi Jianfei, Zhu Shang
Gas-liquid spontaneous imbibition in microchannels is a widely occurring physical phenomenon in nature and many industrial fields. The dynamic contact angle is the key factor affecting the whole gas-liquid imbibition process. In this work, we use a modified pseudopotential multiphase flow (lattice boltzmann method) (LBM) to capture the real-time contact angle during gas-liquid spontaneous imbibition in microchannels and analyze the dynamic characteristics of the contact angle and its effects on the imbibition length. Firstly, we coupled the Peng-Robinson (PR) equation of state to the original pseudopotential multiphase flow LBM, improved the fluid-fluid interaction force and fluid-solid interaction force formats, and added the external forces to the LBM framework by using the exact difference method. Then, the accuracy of the model was verified by calibrating the thermodynamic consistency of the model and simulating interfacial phenomena such as interfacial tension and static equilibrium contact angles. Finally, based on the established simulation method, the spontaneous gas-liquid percolation process in the microchannel is simulated in the horizontal direction. The results show that the contact angle in the imbibition process is dynamic and varies greatly in the early stage of imbibition due to the inertia force. With the further increase of the imbibition distance, it gradually decreases and tends to the static equilibrium contact angle. The contact angle in the imbibition process is related to the microchannel size and the static contact angle. As the width of the microchannel increases, the difference between the dynamic contact angle and the static contact angle in real-time increases; as the static contact angle increases, the difference between the dynamic contact angle and the static contact angle in real-time increases. In addition, the Lucas-Washburn (LW) equation, which ignores the dynamic contact angle, predicts the position of the meniscus is different from the simulated results. The real-time dynamic contact angle data obtained from the simulations can be directly applied to correct the LW equation, and the corrected LW equation predicts the position of the meniscus in general agreement with the simulated results.
, Available online  , doi: 10.6052/0459-1879-22-409
Qin Zhiwei, Liu Zhen, Gao Haibo, Sun Guangyao, Sun Cong, Deng Zongquan
Cable-driven parallel robots (CDPRs) represent a class of particular parallel robots whose rigid links are replaced by cables, where cable can only generate pull force and cannot be compressed. The force distribution in cables is one of the core problems for redundant CDPRs. The hybrid joint-space control strategy, where the chosen redundant cables are force-controlled, whereas the remaining ones are length-controlled in the joint space, is the main type of control strategy discussed in this paper. Because different cable combinations may lead to different control effects. This study provides the selection criteria for the target force-controlled cable combination in the hybrid-input control strategy. The cable tensions in the space with tension vectors as basis for two redundancies for cable-driven parallel robots were expressed based on the equivalent transformation method of vector space basis. The acceptable cable force errors limit proposed in this paper (CFEL) were defined and calculated based on the cable tensions in the space with tension vectors to find appropriate cable combinations for the force control. To validate the analysis of the force-distribution characteristics, a hybrid-input control trajectory planning strategy was developed using multibody dynamics simulations, based on a suspended cable configuration with layouts including two redundancies, while considering the interference of cable length and cable forces. In addition, a fix-pose simulation case via hybrid-input control strategy was performed to validate accuracy of the proposed calculation method for the CFEL. Finally, we found that cable combinations play an essential role for force control as the force control errors may be significantly magnified in cable combinations with high force-distribution sensitivity characteristics. The simulation results illustrate the significance of the analysis in this paper. What’s more, the concept of CFEL proposed in this paper provides guidance for the design of cable force controllers under the control strategies of hybrid joint-space input.
, Available online  , doi: 10.6052/0459-1879-22-463
Li Chunfeng, Zhao Xueting, Duan Wei, Wu Tao, Yao Zewei, Chen Guoxin, Li Gang, Peng Xi
Focusing on the national strategic goal of "Carbon Peaking and Carbon Neutrality", this paper comprehensively analyzes the strategic conditions and targets suitable for large-scale CO2 geo-storage in the China offshore basins, from the perspectives of fault activity, basin pressure, tectonic subsidence, seismicity, and geothermal gradient. It is considered that the East China Sea Shelf Basin, Pearl River Mouth Basin, eastern Qiongdongnan Basin, and the central South China Sea basin are the best geological storage areas for CO2, although this does not exclude suitable targets in other unfavorable sedimentary basins since a specific geo-sequestration target is small in area. The suitable CO2 storage strata in the East China Sea Shelf, Pearl River Mouth, and Qiongdongnan Basins include the bottom salt-water layer of the late rapid subsidence sediments in the open-sea environment and the hydrocarbon-bearing units in the thermal subsidence sedimentary sequences. Between 800 and 4000 m depths beneath the seafloor, the porosity is greater than 10%, and the hydrostatic and lithostatic pressures vary from ~ 8 to ~ 40 MPa and from ~ 13 to ~ 83 MPa, respectively. In this pressure and suitable geothermal gradient ranges, CO2 exists in a supercritical state, and its density is relatively stable with temperature and pressure changes, which is beneficial to the flow and permeation of CO2. The scale and number of mafic magmatic rock formations in the basins also provide good conditions for CO2 geological sequestration and permanent mineralization. Although operationally difficult and expensive, CO2 storage in the central South China Sea basin is very safe. CO2 injected deep into the oceanic basalt can undergo basalt mineralization, but if CO2 is escaped as the mineralization process is relatively slow, escaped CO2 can be further trapped by multiple other storage processes, including pyroclastic rock mineralization, seafloor sediment sequestration, seabed sediment CO2 hydrate storage, carbonate neutralization reaction, seabed carbon lake, ocean dissolution, etc. The existing six International Oceanic Discovery Program (IODP) boreholes that have encountered basement basalt in the central basin of the South China Sea can provide a good scientific and engineering foundation for the pilot CO2 storage experiment in the South China Sea basin.
, Available online  , doi: 10.6052/0459-1879-22-384
Wang Zhechao, Jia Wenjie, Feng Xiating, Wang Jingkui
Tunnel lined cavern gas storage is a new energy storage method, which helps balance supply and demand, promotes the continuous transition from fossil energy to green energy, and facilitates the realization of national goal of "carbon neutralization and carbon peak". In this paper, the ultimate equilibrium method and the elastoplastic analysis method are used to derive the analytical solution of the ultimate storage pressure of tunnel lined rock cavern gas storage. In the ultimate equilibrium method, the self-weight of the overlying surrounding rock, the force of the fracture surface and the ultimate storage pressure are considered, the rigid cone model is selected, and the upper limit pressure expression is derived. In the elastoplastic analysis method, according to the stress distribution law and shear and tensile strength in the surrounding rock, the upper and lower pressure expressions under elastoplastic conditions are derived. Finally, the analytical solution of the ultimate pressure is determined with considering the results obtained by the two methods. The results show that the relationship between the upper limit pressure and the buried depth is quadratic function, and increases with the increase of lateral pressure coefficient; The upper limit pressure and lower limit pressure determined by the elastoplastic analysis method are linear with the burial depth, and the lower limit pressure decreases with the increase of the lateral pressure coefficient, and the lower limit pressure is not considered for the lined gas storage under the condition of class I surrounding rock. When the lateral pressure coefficient is 1.2, the upper limit pressure is the largest, so the tunnel type gas storage should be built as far as possible under the surrounding rock condition with the lateral pressure coefficient of 1.2. Finally, the recommended pressure ranges of lined rock caverns are given according to the upper and lower limit pressure curves under typical working conditions.
, Available online  , doi: 10.6052/0459-1879-22-474
Liu Yuewu, Fang Huijun, Li Longlong, Ge Tengze, Zheng Taiyi, Liu Danlu, Ding Jiuge
Clean and efficient coal utilization becomes an important direction and new research topic under the dual-carbon background. Recently, underground coal gasification (UCG) develops very fast and shows great potential in this area. However, the laboratory and field experiments, which are usually used to investigate the gasification mechanisms and optimize the operating parameters, are quite expensive. Thus, there is a strong demand for the numerical approach that is low-cost, easy operation, and short-cycle. Currently, the numerical approach faces challenges in terms of mathematical modelling and numerical method for solving the nonlinear system because of the complexity of the gasification process. To deal with that, we have done the work as follows: clarified the materials and key problems in each space based on a detailed analysis and revealed the essence of the UCG; summarized four kinds of key mechanical issues including fluid dynamics, thermodynamics, material mechanics, and chemical reaction kinetics; reviewed the development history of numerical research for key mechanical problems in detail and introduced the latest results; illustrated the status of engineering application of numerical research and pointed out the development trends. The work in this paper has positive theoretical significance for the development of the numerical technique for UCG and guiding the design and implementation of UCG trials in China.
, Available online  , doi: 10.6052/0459-1879-22-331
Li Xikui, Zhang Songge, Chu Xihua
The definition of effective pressure with associated formula of the Bishop parameter for unsaturated porous medium proposed in the frame of the theory of macroscopic porous continuum has been controversial for a long time. This also affects the correct prediction of directly related generalized Biot effective stress. Based on the Voronoi cell model described with the discrete system composed of solid particles, binary bond liquid bridges and liquid films, the present paper presents the definitions of effective internal state variables at local material points in unsaturated porous continua with low saturation, i.e. effective pressure and generalized Biot effective stress. Using the proposed Voronoi cell model, their expressions are formulated with the information of hydro-mechanical meso-structure and moso-response evolved with incremental loading process exerted on the representative volume element (RVE) of unsaturated granular material. With the derived effective pressure formula, it is demonstrated that the effective pressure tensor of unsaturated porous continuum is anisotropic. It has not only an anisotropic effect on hydrostatic components, but also an effect on shear stress components, of generalized Biot effective stress tensor. It is demonstrated that the fundamental defect of both the generalized Biot theory and the so-called bivariate theory lies in that it is assumed that effective pore pressure tensor representing the hydro-mechanical effect of two immiscible pore fluids on the solid skeleton of unsaturated porous continua is isotropic. In addition, the Bishop parameter introduced as the weighted factor to define the isotropic effective pore pressure tensor is assumed not related to the matrix suction with very important effect on the hydro-mechanical response occurring at local material points over unsaturated porous continua. The derived formulae of both generalized Biot effective stress and effective pressure (including effective Bishop parameter reflecting the isotropic effect of effective pressure) can be upscaled to a local material point, where the RVE is assigned, in macroscopic unsaturated porous continua, for computational multi-scale methods represented by the concurrent computational homogenization method for unsaturated granular materials.
, Available online  , doi: 10.6052/0459-1879-22-407
Liu Xiyan, Luo Kai, Yuan Xulong, Ren Wei
The expansion stern is an important factor affecting the flatting trajectory and its stability of a trans-media vehicle during high speed water entry and turning flat process. In this paper, based on the fluid volume multiphase flow model and dynamic mesh technology, the coupling calculation method of multiphase flow field and trajectory of the trans-media supercavitating vehicle entering water at high speed is established. The accuracy and applicability of the numerical calculation method are verified by the experiments. Through the numerical simulation study on the high speed water entry and turning flat process of the trans-media vehicle, the influence of the expansion stern on the cavity development morphology, hydrodynamic characteristics and trajectory characteristics of the vehicle during the water entry and turning flat process is obtained, and the influence of the cone angle of expansion sterns on the flatting trajectory during high speed water entry is analyzed. The results show that when the vehicle without the expansion stern entering water and turning flat under the different preset rudder angles, the angle of attack increases continuously, eventually leading to the divergence of the flatting trajectory. After the vehicle with the expansion stern entering water, the recovery moment is formed when the expansion stern is wetted, and the stable flatting trajectory is obtained. The vehicles with different expansion stern cone angles (1.5°, 6°, 8°) have formed three different kinds of trajectory characteristics: stable planing, single-sided tail-slapping and double-sided tail-slapping, and all of them can achieve stable flatting trajectory. The principle of stable planing trajectory is the dynamic balance under the coupling effect of the preset rudder angle and expansion stern planing. This trajectory has the smallest comprehensive drag coefficient, the highest flatting efficiency and the smallest dynamic load, which is an ideal flatting trajectory form for the trans-media vehicle during high speed water entry.
, Available online  , doi: 10.6052/0459-1879-22-427
Jia Haowei, Yu Haiyang, Xie Feifan, Yuan Zhou, Xu Ke, Wang Yang
CO2 microbubble is a promising enhanced oil recovery and carbon sequestration method. In this paper, based on microbubbles porous media generation method, a self-designed microbubble generator featuring the porous ceramic membrane was developed. The morphology and dissolution characteristics of CO2 microbubbles at different initial CO2 concentrations were experimentally investigated. The results showed that the CO2 microbubbles prepared at 10 MPa were distributed in the range of 10 ~ 70 μm with an average bubble diameter of 34.43 μm. At 15 MPa, CO2 microbubbles with smaller diameter were generated, with an average bubble radius of 25.03 μm. However, under high salinity condition, microbubbles with average diameter of 277.17 μm were produced. The brine salinity decreased microbubbles stability, which leading to bigger bubble. In a word, the microbubbles diameter was highly affected by the pressure in microbubbles porous medium generation method. Then, the static and dynamic dissolution kinetics of microbubbles in the porous media were investigated by microfluidics. The results of dissolution experiments showed that microbubbles had excellent dissolution efficiency. When contacting with formation water, microbubbles would rapidly dissolve and the undissolved microbubbles were still migrating the porous media in the form of bubbles. CO2 microbubbles could form a migration mode with carbonated water in the front and microbubbles in the rear, after microbubble were injected into the reservoir. For the first time, the enhanced oil recovery mechanisms of CO2 microbubbles were studied under high-temperature high-pressure conditions, which mainly include: ①Microbubbles carry residual oil on the pore wall during migration; ②Microbubbles carry residual oil droplets out of the pores with dead ends through dissolution and oil swelling; ③Break the capillary force balance of residual oil droplets and promote the flow of oil droplets; ④Block the high permeability channel to improve the sweep efficiency. This paper provides valuable guidance for CO2 microbubble to enhanced oil recovery and carbon sequestration.
, Available online  , doi: 10.6052/0459-1879-22-507
Wang Monan, Jiang Guodong, Liu Fengjie
Aiming at the problems that there is a certain difference between the muscle fiber microstructure model and the image observed under the microscope, the microscopic component biomechanical model cannot effectively capture the mechanical behavior of skeletal muscle during shear deformation, and the high calculation cost of multi-scale numerical models of skeletal muscle. In this thesis, the mechanical properties of skeletal muscle are studied from the perspectives of experiment, multiscale modeling and simulation. Curved-edge Voronoi polygons are proposed as the cross-section of muscle fibers, and the corresponding representative volume element (RVE) is established at the microscale. A new biomechanical model (MMA model) is proposed, and the MMA model is used as the biomechanical model of muscle fibers and connective tissue, the MMA model adopts complete strain invariants$ {I}_{4}、{I}_{5}、{I}_{6}、{I}_{7} $, so that the shear behavior of skeletal muscle is reflected at the level of material properties. Combine the experimental results of skeletal muscle, the RVE models, the biomechanical models of muscle fibers and connective tissue to establish a multiscale numerical model of skeletal muscle. According to the experimental results, the parameters of the biomechanical model are determined, the multiscale homogenization method are used to realize the connection between the microscale and the macro-scale, and the macroscopic mechanical behavior of skeletal muscle is finally obtained, four deformation forms of Longitudinal stretch, stretch laterally, out-of-plane longitudinal shear and in-plane shear are performed to verify the convergence of the model. This thesis research the effects of model parameters, muscle fiber volume fraction and muscle fiber structure on skeletal muscle on macroscopic mechanical behavior. Combined with experimental data, the effectiveness of the multiscale numerical model is verified. In this paper, the multi-scale numerical model of skeletal muscle can not only be used to study the influence of microscopic factors on the macroscopic mechanical behavior of skeletal muscle, but also to study the influence of diseases on the biomechanical properties of skeletal muscle and to simulate skeletal muscle remodeling and regeneration.
, Available online  , doi: 10.6052/0459-1879-22-496
Zheng Zhiyue, Jiang Zhansi, Ding Zeliang, Du Wangfang, Li Kai, Chen Xue
The fin-tube heat exchanger is common in the refrigeration industry. The expansion forming mechanism of the heat tube is of significant importance for refrigeration equipment, which determines its mechanical property and heat transfer performance. In this paper, a three-dimensional fluid-solid coupling model of the tube-fin heat exchanger is proposed. By using a unidirectional fluid-solid coupling transient method, the flow behaviors and deformation characteristics of the fluid and solid domains are numerically studied. Results show that the reasonable range of pneumatic expansion pressure is verified to be P = 12.5 MPa, which is consistent with the value derived from the theoretical equations. According to the variations of tube and fin stresses with time, the tube stresses at different fin-tube joints are greater than their yield limit of 66 MPa, and the fin stresses at different fin-tube joints are slightly greater than their yield limit of 132 MPa, which agree with the requirements of expansion forming process. After expansion, the average tube diameter increases with the pressure increases. The radial displacement of the heat exchanger tube is smaller in the horizontal direction and larger in the vertical direction, and the difference between maximum and minimum displacement is about 0.03 mm. The variation of the residual contact pressure with different expansion pressures was investigated, which exhibits three stages. When P < 11 MPa, the residual contact pressure increases with the expansion pressure. If 11 < P < 12.5, the residual contact pressure decreases with the increase of expansion pressure. While P > 12.5 MPa, the residual contact pressure stabilizes at 0.7 MPa. The numerical results indicate that when the expansion pressure makes the inner hole of the fin yield, increasing the expansion pressure will lead to incomplete expansion. Finally, the effect of holding time is studied, which show that changing the holding time has little effect on the expansion quality. The relevant results provide theoretical guidance for the actual engineering of the small fin-tube heat exchanger in the pneumatic expansion process.
, Available online  , doi: 10.6052/0459-1879-22-482
Wang Peng, Yang Shaopu, Liu Yongqiang, Liu Pengfei, Zhao Yiwei, Zhang Xing
To explore the lateral instability of the wheelset system, the gyroscopic effect and the influence of the primary suspension damping are considered, a dynamic model of the wheelset system with a nonlinear wheel-rail contact relationship is established, and the hunting stability, Hopf bifurcation characteristics, and migration transformation mechanism are investigated. The hunting instability critical speed of the wheelset system is obtained through the stability criterion. The central manifold theorem is used to reduce the dimensions of the wheelset system. Then the reduced wheelset system is simplified using the normal form method to obtain a one-dimensional complex variable equation with the same bifurcation characteristics as the wheelset system. The expression of the first Lyapunov coefficient of the wheelset system is derived theoretically, and the Hopf bifurcation type of the wheelset system can be judged according to its sign. The influence of different parameters on the Hopf bifurcation critical speed of the wheelset system is discussed, and the distribution law of supercritical and subcritical Hopf bifurcation regions of the wheelset system in two-dimensional parameter space is explored. Three typical Hopf bifurcation diagrams of the wheelset system are obtained by numerical simulation, which verifies the correctness of the distribution law of the supercritical and subcritical Hopf bifurcation regions of the wheelset system. The results reveal that the critical speed of the wheelset system decreases with the increase of the equivalent taper, increases with the increase of the longitudinal stiffness and longitudinal damping of the primary suspension, and first increases and then decreases with the increase of the longitudinal creep coefficient. The change of system parameters will change the type of Hopf bifurcation of the wheelset system, that is, the subcritical and supercritical Hopf bifurcations migrate and transform each other. The distribution law of the Hopf bifurcation domain of the wheelset system in two-dimensional parameter space has a certain guiding significance for wheelset parameter matching and optimization design.
, Available online  , doi: 10.6052/0459-1879-22-469
Zhang Xin, Wang Xunnian
Flow control technology using dielectric barrier discharge plasma actuators which are driven by a sinusoidal alternating current high-voltage power is an active flow control technology based on plasma actuation and has some advantages, such as short response time, simple structure, low consumption power, and no need for additional air source devices. It has broad application prospects in lift enhancement and drag reduction, vibration suppression and noise reduction, assisted combustion and anti-icing. In view of the three problems that most of the power consumed by the plasma actuator has not been exploited, the whole evolution process of the induced flow field has not been fully understood, and the evolution mechanism of the induced flow field is not clear, the present manuscript summarizes the research progress of the induced flow field of the plasma actuator from the three aspects which include the spatial structure, the space-time evolution process and the evolution mechanism of the induced flow field of the plasma actuator. For flow structures of the induced flow field, the turbulent characteristics of induced wall jet under high voltage excitation are found, and the correlation mechanism between coherent structure in the vicinity of wall and non-dimensional actuation parameters is analyzed; The potential energy of the plasma actuator is excavated from the aspect of the acoustic energy induced by the plasma actuator, and the new phenomenon of "the ultrasound and the acoustic streaming flow created by the plasma actuator" is found, and the novel mechanism of acoustic excitation created by the plasma actuators is proposed; In the aspect of the spatial-temporal evolution process, the complete evolution process of the flow field induced by the plasma actuator from the thin wall jet to the "arch" jet, then to the starting vortex, and finally to the quasi-steady wall jet is uncovered; In terms of the evolution mechanism, the evolution mechanism of the induced flow field is proposed based on the acoustic characteristics. In addition, to break through the bottleneck of flow control technology using plasma actuators and open up the innovation link of "concept innovation - technology breakthrough - demonstration and verification", a few opening issues on the flow field generated by the plasma actuators are presented.
, Available online  , doi: 10.6052/0459-1879-22-377
Han Fang, Wang Qingyun
Neurodynamics is a foundational branch of dynamics and control, which belongs to the international frontier of the interdisciplinary field of mechanics, brain science and intelligence science. Based on the basic theories and methods of dynamics and control, the study of neurodynamics mainly focuses on establishing reasonable models to explore the mechanisms of electrophysiological dynamic behaviors of nervous system and brain cognitive functions. In recent years, scholars at home and abroad have obtained remarkable achievements in the foundational research of neurodynamics, including the in-depth study of the dynamical behavior of neurons and neural networks, the modeling and analysis of different functional structures of the brain, and the network dynamics modeling and control of brain regions associated with nervous disease. In this paper, we firstly overviewed elaborately the recent advancements in the field of neurodynamics. Especially, development history for advancement of neural modeling is exhibited. Then, by analyzing the research outcomes of biological neural networks and their dynamics, some thoughts and prospects for future research are put forward. It is expected that neurodynamics will contribute to the breakthroughs of the theories and methods of brain-like intelligence and intelligent equipment with strong interpretability and generalization ability, and finally their applications in major engineering projects.
, Available online  , doi: 10.6052/0459-1879-22-404
Zhao Xinxin, Shi Jinguang, Wang Zhongyuan, Zhang Ning
To research the dynamic stability of fixed canard dual-spin projectiles in full trajectory flight, the state space model of the complex attack angle motion is established under the condition of small attack angle, and the general condition that the real parts of the characteristic roots are all negative is derived by using the Hurwitz method. Based on the motion characteristics of the front body’s rolling angle before/after starting control, the dynamic stability criterion of fixed canard dual-spin projectiles under different flight conditions is proposed by using the stability analysis method of the conventional rotating projectiles, whose form is similar to that of the conventional rotating projectiles. When flying without control, the control force and moment terms of control canard are added correspondingly in the lift force and static moment terms. Controlled flight further increases the relative increment effect of relevant terms. Accordingly, the constraint on canard parameters of control surface is deduced under the condition that the parameters of projectile body are determined, the effects of the control force coefficient’s derivative, the installation position and the deflection angle of control canard on the dynamic stability are discussed, and the reasons for the formation of the dynamic instability of this kind of projectile are revealed. The simulation analysis results of the complex attack angle motion under different conditions show that when the relative increment caused by control surface is within the boundary of both uncontrolled and controlled flight, the full trajectory flight of the fixed canard dual-spin projectile is dynamically stable, which verifies that the dynamic stability criterion and the constraint on canard parameters deduced in this paper are reasonable and feasible, and provides a theoretical basis and design reference for the design and development of this type of projectile.
, Available online  , doi: 10.6052/0459-1879-21-636
Wang Fangjian, Wang Hongwei, Li Xiaohui, Dong Lei, Huang Zhan, Chen Lan
As the main means of attack in modern air combat, air-to-air missile requires higher maneuverability and agility than target aircraft. What’s more, in the face of the new generation of aircraft, the new air-to-air missile must possess all-round attack capability, especially to the threat from the rear target. Therefore, advanced and efficient maneuver methods such as higher turning rate and larger maneuver envelope are needed. In order to ensure the successful completion of efficient maneuvering, the new advanced air-to-air missile is required to have flight and maneuvering control capability within the range of extra-wide angle-of-attack (α = 0° ~ 180°). In the past, most of the observation and research on unsteady flow with extra-wide large angle-of-attack were concentrated in the range α = 40° ~ 60°, and the maximum angle-of-attack was less than 90°. In this paper, numerical simulation (delayed detached eddy simulation, DDES) and wind tunnel test in FD-12 (oil-flow visualization experiment) are used to study the transient flow characteristics and unsteady characteristics in Mach number 0.6 at the angle-of-attack of α = 0° ~ 180° of the slender revolutionary body. At the angle-of-attack of α = 0° ~ 90°, the flow on the leeward side of the slender revolutionary body is mainly dominated by concentrated vortices caused by cylindrical segments, which are characterized by asymmetric vortice, unsteady vortice and vortex shedding. At the angle-of-attack of α = 90° ~ 180°, the bottom of the slender revolutionary body is forward, which leads to a large separation area, and many small-scale eddy interaction in the separation area. As the flow gradually develops backward along the axial direction, the leeward flow is gradually dominated by asymmetric vortex flow. The frequency St number of surface fluctuating pressure induced by asymmetric vortices ranges from 0.19 to 0.33, and the frequency St number of surface fluctuating pressure induced by bottom separation region ranges from 1.55 to 1.64.
, Available online  , doi: 10.6052/0459-1879-21-415
Zhao Yaobing, Zheng Panpan, Chen Lincong, Kang Houjun
Symmetry is one of the five aesthetic characteristics in the vibration theory, but the symmetry-breaking is also inevitable. This paper takes a common vulnerable structure in engineering-the suspended cable-as an example, and the influences of symmetry-breaking on the planar coupled vibrations have been investigated when the asymmetric damage is occurred. Firstly, the in-plane nonlinear dynamical model of damaged suspended cable has been established, and the nonlinear infinite dimensional differential equations have been obtained by using the Galerkin method. The method of multiple scales has been adopted to obtain the modulation equations of the nonlinear systems’ in-plane coupled vibrations. The resonant curves of undamaged and damaged suspended cables including the first nine modes have been obtained by using the numerical methods, and the stabilities of solutions have also been determined. The largest Lyapunov exponent has been calculated to determine the system’s chaotic motions. The numerical results show that the classical parabolic curves have been often adopted to simulate the suspended cables’ static configurations. However, when the asymmetric damage occurs, the piecewise functions should be used to accurately describe the damaged cables’ static configurations. The symmetry-breaking causes crossover points between two natural frequencies of suspended cables to turn into veering points, and the symmetric/anti-symmetric mode shapes before damage are changed into the asymmetric ones after damaged. The nonlinear interaction coefficients are changed significantly, resulting in significant changes in internal resonant responses. When the excitation is directly applied to the higher-order modes, the single-mode solutions and internal resonant ones are obvious in the undamaged system, while the damaged system does not present the obvious single-mode solutions. The bifurcations and chaos of the damaged system are also changed obviously, and some chaotic motions around the period-doubling bifurcation are observed as to the damaged system.
, Available online  , doi: 10.6052/0459-1879-21-542
Wan Zheng, Cao Wei, Liu Yuanyuan, Zhang Hongfen
K0 consolidated clay is widely distributed in nature. It usually has both overconsolidation property and natural structural property, and it is a significant difference for the property of overconsolidation of K0 to the normal consolidation of K0 clay. In order to effectively describe the overconsolidation properties of K0 consolidated clay, three improvements were made on the basis of the natural structure consolidated model for clay, so that the original model can be extended to a constitutive model that consider both the properties of K0 overconsolidation clay and the effects of natural structures for natural clay. (1) The relative stress ratio is introduced into the yield surface equation to describe the yield property, and the initial anisotropic consolidation stress ratio parameter ξ is introduced into the yield surface equation to express the influence of the initial anisotropy on the position of the yield surface in p-q space. (2) Based on the given yield surface equation, the phase transformation stress ratio parameter was derived, and the phase transformation stress ratio was introduced into the unified hardening parameter. The unified hardening parameter can effectively describe both the initial anisotropic shearing behavior and the dilatancy behavior, strain hardening and softening phenomenon for initial anisotropic consolidated clay. (3) The cementation parameter pe, which reflects the structural cementation, is introduced into the yield surface equation and the decay evolution equation of pe with deviatoric plastic strain is given. The dilatancy properties of structural clay can be described by using the cementation parameter. The comparison between the prediction and the test results shows that the proposed K0 consolidation model can effectively describe the stiffness enhancement effect of K0 overconsolidated clay, the Bauschinger effect of clay, the cementation strength loss phenomenon and the strain softening phenomenon of structural clay. The applicability and rationality of the proposed model are proved.
, Available online  , doi: 10.6052/0459-1879-21-265