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Table of Content

    28 September 2024, Volume 29 Issue 5 Previous Issue   

    Naval Architecture, Ocean and Civil Engineering
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    Naval Architecture, Ocean and Civil Engineering
    Ship Pipe Layout Optimization Based on Improved Particle Swarm Optimization
    LIN Yan1, 2(林焰), BIAN Xuanyi1(卞璇屹), DONG Zongran3(董宗然)
    2024, 29 (5):  737-746.  doi: 10.1007/s12204-022-2530-6
    Abstract ( 57 )   PDF (1456KB) ( 51 )  
    Ship pipe layout optimization is one of the difficulties and hot spots in ship intelligent production design. A high-dimensional vector coding is proposed based on the research of related pipe coding and ship pipe route features in this paper. The advantages of this coding method are concise structure, strong compatibility, and independence from the gridding space. Based on the proposed coding, the particle swarm optimization algorithm is implemented, and the algorithm is improved by the pre-selected path strategy and the branch-pipe processing strategy. Finally, two simulation results reveal that the proposed coding and algorithm have feasibility and engineering practicability.
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    Experimental Study and Numerical Simulation of Evacuation in an Offshore Platform
    ZHANG Jingjinga (张菁菁), ZHAO Jinchenga, b, c∗(赵金城), SONG Zhensena, b, c (宋振森), DUAN Lipinga, b, c(段立平)
    2024, 29 (5):  747-758.  doi: 10.1007/s12204-023-2629-4
    Abstract ( 31 )   PDF (4007KB) ( 16 )  
    With the rapid development of marine oil and gas exploitation, the evacuation of offshore platforms has received more attention. First, an experimental investigation of the evacuation process of 120 participants in a real offshore platform is performed, and then simulation results provided by Pathfinder are validated against the measurement results. Second, four typical evacuation scenarios on the platform referring to IMO guidelines are investigated by Pathfinder with the speed values achieved in experiments. The simulation results show that both the utilization of exits and evacuation efficiency of people on the offshore platform need to be further improved. Last, the evacuation routes of people under the four scenarios are optimized, and the improvement of the evacuation performance after the optimization is evaluated by several mathematical indicators. Final results show that the evacuation with the optimized route design prompts the use efficiency of exits and further reduces the evacuation time. The present study provides a useful advice for potentially revising the IMO guidelines in future and provides efficient evacuation strategies for planning the emergency evacuation on offshore platforms.
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    Knowledge-Based Curved Block Construction Scheduling and Application in Shipbuilding
    JIANG Zuhua1∗(蒋祖华), ZHOU Hongming2(周宏明), TAO Ningrong3(陶宁蓉), LI Baihe1(李柏鹤)
    2024, 29 (5):  759-765.  doi: 10.1007/s12204-022-2544-0
    Abstract ( 18 )   PDF (1037KB) ( 12 )  
    To increase efficiency in fierce competition, it is necessary and urgent to improve the standard of production planning for shipbuilding. The construction of curved blocks is the bottleneck to improve the efficiency of shipbuilding. Thus it is a key breakthrough for higher shipbuilding productivity to study the curved block production. By analyzing the scheduling problem in curved blocks production, we propose an intelligent curved block production scheduling method and its system based on a knowledge base, and show the main process of the system. The functions of the system include data management, assembly plan generation, plan adjustment, and plan evaluation. In order to deal with the actual situation and inherit the empirical knowledge, the system extracts some rules to control block selecting, algorithm selection, and evaluation thresholds to build a production decision-making knowledge base in the curved block scheduling system. The proposed knowledge base could be referred and modified by users, especially after a few interactions between the users and the knowledge base. The final assembly plan can be visualized and evaluated to facilitate the observation of plan implementation and effects of the decisions in the process. Finally, the system is verified by a large shipyard in Shanghai using real data and the results illustrate that the proposed method can perform the knowledge-based scheduling for curved blocks construction effectively.
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    Attitude Stabilization of Unmanned Underwater Vehicle During Payloads Release
    DENG Xua (邓旭), FENG Zhengpinga, b∗ (冯正平), HE Chenlua (何晨璐), CUI Zhenhuaa (崔振华)
    2024, 29 (5):  766-772.  doi: 10.1007/s12204-023-2598-7
    Abstract ( 19 )   PDF (765KB) ( 10 )  
    Large unmanned underwater vehicles can carry big payloads for varied missions and it is desirable for them to possess an upright orientation during payload release. Their attitude can hardly be maintained during and after the phase of payload release. Releasing a payload from the vehicle induces uncertainties not only in rigid-body parameters, e.g, the moment of inertia tensor due to the varying distribution of the masses on board the vehicle, but also in the hydrodynamic derivatives due to the vehicle’s varying geometric profile. A nonlinear attitude stabilizer that is robust to these time-varying model uncertainties is proposed in this paper. Stability is guaranteed via Lyapunov stability theory. The simulation results verify the effectiveness of the proposed approach.
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    Neural Network Optimization of Multivariate KDE Bandwidth for Buoy Spatial Information
    XU Liangkun1, 2 (徐良坤), XUE Han2∗ (薛晗), JIN Yongxing1 (金永兴), ZHOU Shibo2 (周世波)
    2024, 29 (5):  773-779.  doi: 10.1007/s12204-022-2466-x
    Abstract ( 27 )   PDF (731KB) ( 13 )  
    It is one of the responsibilities of the navigation support department to ensure the correct layout position of the light buoy and provide as accurate position information as possible for ship navigation and positioning. If the position deviation of the light buoy is too large to be detected in time, sending wrong navigation assistance information to the ship will directly affect the navigation safety of the ship and increase the pressure on the management department. Therefore, mastering the offset characteristics of light buoy is of great significance for the maintenance of light buoy and improving the navigation aid efficiency of light buoy. Kernel density estimation can intuitively express the spatial and temporal distribution characteristics of buoy position, and indicates the intensive areas of buoy position in the channel. In this paper, in order to speed up deciding the optimal variable width of kernel density estimator, an improved adaptive variable width kernel density estimator is proposed, which reduces the risk of too smooth probability density estimation phenomenon and improves the estimation accuracy of probability density. A fractional recurrent neural network is designed to search the optimal bandwidth of kernel density estimator. It not only achieves faster training speed, but also improves the estimation accuracy of probability density.
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    Numerical Study of Wave Energy Converter Platform Geometry Layout Design
    PEI Feia (裴斐), LIN Yanb∗ (林焰)
    2024, 29 (5):  780-790.  doi: 10.1007/s12204-022-2483-9
    Abstract ( 17 )   PDF (2088KB) ( 9 )  
    The present work is aimed at determining the optimal geometry layout of a wave energy converter platform for plate energy harvesting performance. A linear potential fluid theory method was applied to analyzing the interaction between the platform and plate. Three factors of layout geometry were tested and the performance of the plate was analyzed. The methodology of design of experiments was used to confirm factor significance and build response surface model. The 1st order model and the 2nd order model were built to describe the relation between factors and plate performance. The significance of two factors and their interactions were revealed, and an optimal parameter set was found. The wave form in front of the plate confirmed the interactions. It is clear that a wide entrance and enclosing channel for waves can maximize the plate performance.
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    Optimization of Highway-Railway Level Crossing in Port Area with Priority of Key Lanes
    ZHANG He(张赫), ZHOU Zhengkai(周正凯), LIN Huanyu(林环宇), WANG Tianci(王天慈)
    2024, 29 (5):  791-800.  doi: 10.1007/s12204-022-2553-z
    Abstract ( 23 )   PDF (689KB) ( 9 )  
    When controlling the signal of highway-rail level crossings in the port area, the multi-objective signal optimization model is not applicable due to the cross effect of roads and railways and the priority of incoming vehicles. Therefore, in order to ensure that the inbound truck fleet enters the port directly without being affected by the train when passing through the highway-rail level crossing in the port area, the queuing of vehicles in front of the port needs to be reduced, and the priority should be given to the inbound trucks. Based on the idea of priority on key lanes, this study relies on speed guidance information to guide the fleet to shift reasonably, postpone or early arrive at the railway gate. At the same time, the optimization goal is to minimize the delays at intersections, the number of stops, and the vehicle exhaust emissions. The measured data of road-rail level crossings in Dayaowan Port Area of Dalian were selected, and it was re-developed under the VISSIM environment by serial interface to realize signal optimization control under vehicle speed guidance. The original timing plan, multi-objective timing optimization plan and key lanes priority are given to the optimization scheme for simulation experiments. The results show that the multi-objective optimization scheme and the optimization scheme under the priority of key lanes can generally improve the traffic capacity of road-rail level crossings. Compared with the original plan, the optimization plan under the priority of key lanes reduces the delay by 33.3%, the number of stops is reduced by 25%, and the vehicle exhaust emissions are reduced by 31.3%. It proves the effectiveness of the optimization scheme for highway-rail level crossings in the port area under the priority of key lanes, and it is more suitable for highway-rail level crossings.
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    Predictive Simulation of External Truck Operation Time in a Container Terminal Based on Traffic Big Data
    DU Ye1 (杜晔), ZHAO Yifei2 (赵一飞), GAO Deyi1 (高德毅)
    2024, 29 (5):  801-808.  doi: 10.1007/s12204-022-2415-8
    Abstract ( 19 )   PDF (620KB) ( 6 )  
    The operation time of external trucks in a container terminal is one of port operation key performance indicators concerned by port operators, external truck operators and related government authorities. With the traffic big data combined with the operation characteristics of the container terminal, the system dynamics method is used to build the simulation model of the operation system for external trucks. The simulation results of the operation time of external trucks are consistent with the actual situation, which provides an effective way to eliminate the “black box” of the operation time of the external trucks. The model can also be applied in multiple scenarios by using the traffic big data, and the simulation results can be adopted by the relevant organizations.
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    CFD Investigations of Interaction Between Freak Wave and Bottom-Mounted Vertical Cylinder
    GAO Ningbo1 (高宁波), ZHANG Yongtao2, 3 (张永涛), ZHANG Hong4 (张鸿)
    2024, 29 (5):  809-816.  doi: 10.1007/s12204-022-2527-1
    Abstract ( 20 )   PDF (1668KB) ( 9 )  
    We studied the interactions between freak wave and bottom-mounted vertical cylinder. The freak wave is generated through linear superposition method which satisfies the definition that the wave height is at least two times the significant wave height. A numerical wave tank is developed based on FLUENT software in which the finite volume method is used for the spatial discretization. Grid sensitivity is conducted in 2D model, and then the freak wave is simulated in 3D model. The freak wave loads on the vertical cylinder are calculated and compared with the results obtained through Morison equation. The numerical results present larger peak and shallower trough compared with the prediction of Morison equation. Meanwhile, the free surface wave elevation within a radius distance around the vertical cylinder is investigated. The lowest wave run-up around vertical cylinder caused by freak wave is about 55% of the highest wave run-up, and the direction is about 45˚of the wave propagation.
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    Static and Fatigue Behavior of Hybrid Bonded/Bolted Glass Fiber Reinforced Polymer Joints Under Tensile Loading
    WANG Jinxiao1 (王进潇), CHENG Bin1, 2, 3∗ (程斌), XIANG Sheng1 (向升), LI Sida1 (李思达), YAN Xingfei4 (闫兴非)
    2024, 29 (5):  817-830.  doi: 10.1007/s12204-023-2650-7
    Abstract ( 15 )   PDF (1892KB) ( 3 )  
    This paper presents the static and fatigue tests of hybrid (bonded/bolted) glass fiber reinforced polymer (GFRP) joints. Nine specimens of single-lap hybrid GFRP joints have been fabricated to study the static and fatigue behaviors in the experimental campaign. The static tests of uniaxial tension loading are first conducted, from which the static ultimate bearing capacities of the joints are obtained. High-cycle fatigue tests are subsequently carried out so that the fatigue failure mode, fatigue life, and stiffness degradation of joints can be obtained. The measuring techniques including acoustic emission monitoring and three-dimensional digital image correlation have been employed in the tests to record the damage development process. The results revealed that the static strength and fatigue behavior of such thick hybrid GFRP joints were controlled by the bolted connections. The four stages of fatigue failure process are obtained from tests and acoustic emission signals analysis: cumulative damage of adhesive layer, damage of the adhesive layer, cumulative damage of GFRP plate, and damage of GFRP plate. The fatigue life and stiffness degradation can be improved by more bolts. The S-N (fatigue stress versus life) curves for the fatigue design of the single-lap hybrid GFRP joints under uniaxial tension loading are also proposed.
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    Rigid-Membrane Method for Determining Stress Distribution of Membrane Structure Based on Laser Scanner System
    ZHANG Xiangyu1 (张翔宇), WANG Shasha1 (王沙沙), GONG Jinghai1 (龚景海), QIU Guozhi1(邱国志), JI Tengfei2(纪腾飞)
    2024, 29 (5):  831-844.  doi: 10.1007/s12204-022-2472-z
    Abstract ( 16 )   PDF (9136KB) ( 4 )  
    The determination of stress distribution is important for the safe use of membrane structures in practical engineering, which is difficult to be obtained by existing measurement methods and analysis methods. This paper proposes a rigid-membrane method to determine the stress distribution of the membrane, which expands the stiffness of the membrane, applies the load of the membrane in equilibrium to the membrane shape of the equilibrium state, and performs nonlinear finite element analysis. The rigid-membrane method inversely acquires the stress distribution of the membrane based only on the shape and load distribution in equilibrium obtained from the numerical simulation of a membrane structure under water loads, and determines the modulus magnitude and mesh size required to rigidize the membrane. The accuracy of the rigid-membrane method is verified by the small differences between the stress distributions obtained from the proposed method and numerical simulations. The equilibrium membrane shape in the actual project can be scanned and reconstructed by the laser scanner system without any pre-processing, and the load is determined by the water level, internal pressure, etc. Based on the actual membrane shape and water load distribution, the rigid-membrane method determines the real stress distribution of the membrane in the test of flat membrane subjected to ponding water, which verifies that the rigid-membrane method is a practical method to determine the stress distribution only by the membrane shape and external load distribution.
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    Strength Optimization and Prediction of Cemented Tailings Backfill Under Multi-Factor Coupling
    HU Yafei(胡亚飞), LI Keqing(李克庆), HAN Bin (韩斌), JI Kun(吉坤)
    2024, 29 (5):  845-856.  doi: 10.1007/s12204-022-2409-6
    Abstract ( 14 )   PDF (2252KB) ( 5 )  
    In order to solve the problem of strength instability of cemented tailings backfill (CTB) under low temperature environment ( 20 ◦C), the strength optimization and prediction of CTB under the influence of multiple factors were carried out. The response surface method (RSM) was used to design the experiment to analyze the development law of backfill strength under the coupling effect of curing temperature, sand-cement ratio and slurry mass fraction, and to optimize the mix proportion; the artificial neural network algorithm (ANN) and particle swarm optimization algorithm (PSO) were used to build the prediction model of backfill strength. According to the experimental results of RSM, the optimal mix proportion under different curing temperatures was obtained. When the curing temperature is 10—15 ◦C, the best mix proportion of sand-cement ratio is 9, and the slurry mass fraction is 71%; when the curing temperature is 15—20 ◦C, the best mix proportion of sandcement ratio is 8, and the slurry mass fraction is 69%. The ANN-PSO intelligent model can accurately predict the strength of CTB, its mean relative estimation error value and correlation coefficient value are only 1.95% and 0.992, and the strength of CTB under different mix proportion can be predicted quickly and accurately by using this model.
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    Load Characteristics and Optimal Layout of Center and Gage Cutters of Rock Formation Compound Tunnel Boring Machine
    ZHANG Kangjian (张康健), HU Zhechuan (胡哲钏), ZHANG Zhiqiang (张志强)
    2024, 29 (5):  857-875.  doi: 10.1007/s12204-022-2532-4
    Abstract ( 12 )   PDF (7928KB) ( 4 )  
    The cutter layout of a full-face tunnel boring machine (TBM) directly affects its tunneling efficiency. The revolving diameter of the center cutter is small, and the double-edged design results in its rock breaking mechanism and force characteristics being significantly different from those of the single-edged cutter. The gage cutter is installed on the transition arc of the cutterhead, and the installation inclination complicates its movement and force. In this paper, by taking sandstone as the research object, the composite rock breaking models of the center cutter group and the gage cutter group of a compound TBM are separately established based on the three-dimensional particle discrete element method. The numerical models are verified by comparing results with the full-scale rotary cutting laboratory test. From the view point of the force characteristics of a single cutter, the propagation of rock cracks between adjacent cutters, the overall mechanical properties of the cutterhead, the load characteristics and layout form of the double-edged center cutter, and the installation angle range of the gage cutter were studied. Results demonstrate that the use of a cross-shaped center cutter layout can reduce the force of a single cutter ring and the overall load of the cutterhead, which is conducive to TBM stability during tunneling. Therefore, it is recommended that a cross-shaped layout for the double-edged center cutter of a rock formation compound TBM should be used. To improve the stability and service life of the cutter, we recommend setting the installation angle of the innermost gage cutter of the rock formation compound TBM to about 9◦, and the installation angle of the outermost gage cutter should not exceed 70◦.
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    Design Method of Anti-Damage and Anti-Crack for Main Parameters of Tunnel Boring Machine Cutter Head
    ZHU Ye (朱晔), CHEN Xiangyu (陈向禹)
    2024, 29 (5):  876-888.  doi: 10.1007/s12204-022-2520-8
    Abstract ( 11 )   PDF (2755KB) ( 2 )  
    In the actual service process of the tunnel boring machine (TBM) cutter head, the fatigue failure of the disc body is serious. Aimed at the problem of premature failure of cutter head due to the extreme service environment and complicated structure of the TBM cutter head, the previous TBM cutter head failure data are combined to establish a method for calculating the space crack growth in this paper. Based on the structure of the TBM cutter head itself, the law of the shape and parameters of the stiffened panels on the crack propagation resistance is studied to further present the method of anti-damage and anti-crack for the TBM cutter head. The results illustrate that the basis and methods for the structural design of the TBM cutter head are put forward.
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    Flexural Behavior of Cross-Connected Brick Masonry Infill Wall Panels Supported on Reinforced Concrete Beam Grids
    BAYOUMI EL-Said Abd-Allah1, 2∗ , MAHMOUD Mahmoud Hassan3 , ARIF Mohammed 1, 4
    2024, 29 (5):  889-899.  doi: 10.1007/s12204-022-2404-y
    Abstract ( 15 )   PDF (3708KB) ( 5 )  
    This paper presents an experimental investigation on the flexural behavior of cross-connected brick masonry infill wall panels supported on reinforced concrete beam grids above and below the walls. The experimental program was comprised of six wall systems. The effect of change in lower beam stiffness relative to the wall and the geometry of the main walls were investigated. From the results of the experimental tests, the increase in the depth of the lower beam grid reduces the deflection, resulting in an increase in the load carrying capacity of the wall. Further, the stiffness of the main walls affects the deflection and the failure load of the cross walls.
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    Optimization of Strength Properties of Reactive Powder Concrete by Response Surface Methodology
    SAKTHIESWARAN N.a∗, MOORTHY N.b, RENISHA M.a, CHINNADURAI M.c
    2024, 29 (5):  900-908.  doi: 10.1007/s12204-023-2612-0
    Abstract ( 16 )   PDF (595KB) ( 2 )  
    The main objective of this study is to optimize the fresh and strength properties of reactive powder concrete incorporated with industrial by-products like ultra-fine ground granulated blast furnace slag as cement substitute and added with coal bottom ash and recycled concrete fines as partial replacement of quartz sand by response surface methodology through design of experiment approach. Totally four responses namely slump, compressive strength (C-28), flexural strength (F-28), and split-tensile strength (S-28) after 28 days of curing period were considered. The statistical study on the reactive powder concrete includes the modeling of regression, normal probability plots, surface plot analysis, and optimization of process variables. The regression models of the considered responses (slump, C-28, F-28, and S-28) were tested. The results obtained from the analysis of variance (ANOVA) and Pareto chart were used to determine the statistical significance of the process variables. The influence of the variables on the responses was studied by means of the surface plot analysis. The optimal proportion of the variables against the responses was obtained through optimization response. The resulted regression equations were in the form of second-order polynomial equation and the prediction of strength properties was found to be in line with the experimental results. The difference of proportion of variance indicated that only 0.43%, 6.42%, 5.15%, and 9.7% of deviations cannot be expressed by the analysis. The ANOVA and Pareto charts represented the high significance and appropriateness of the linear term of slump response and the two-way interaction term of strength responses. The results of the optimization response revealed the optimal proportions of recycled concrete fines and coal bottom ash as 19.15% and 7.02%, respectively
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    Numerical Simulation on Effect of Indenter Radius During Point Load Test
    WANG Zhi1 (王智), OUYANG Yiping1 (欧阳义平), YANG Qi1, 2∗ (杨启)
    2024, 29 (5):  909-918.  doi: 10.1007/s12204-023-2583-1
    Abstract ( 10 )   PDF (2604KB) ( 3 )  
    To investigate the effect of the radius of the spherical heads of the indenter on the results of a point load test, this study uses a discrete element model based on the flat joint contact for numerical simulation. Results show that the discrete element model based on the flat joint model can accurately describe the damage process and size effects of rocks under point loads. Damage of rock samples under the loading of different radii of the indenter can be characterized as vertical splitting damage, and the larger the radius of the indenter is, the larger the damage area. Values of the point load strength of rock samples increase with increasing the radius of the indenter and obey a power function relationship. The results of this study provide a theoretical basis for the selection of the spherical heads of indenters in point load tests and tool design for mechanical rock breaking.
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    Finite Element Analysis of Effects of Improvement of Soil Between Double-Row Piles
    NIE Dongqing1∗ (聂东清), ZHAI Zhiyang1 (翟之阳), ZHANG Wei1 (张威), LI Zhi2 (李志)
    2024, 29 (5):  919-929.  doi: 10.1007/s12204-022-2501-y
    Abstract ( 14 )   PDF (1562KB) ( 5 )  
    Double-row pile (DRP) retaining systems have been widely used in deep excavations in China. Soil between the front and back-row piles (FBP soil) is often improved to decrease the displacement of DRPs in soft soil areas, but the improvement efficiency has rarely been researched. A large and deep excavation supported by a DRP retaining system is introduced, and the effect of FBP soil improvement is discussed by comparing the finite element analysis and the monitoring results. Then, a parametric study of DRP using the finite element method considering the small strain of soil is conducted to investigate the effect of FBP soil improvement. It was shown that the pile deflection and bending moment decrease when the FBP soil is improved. Moreover, the most efficient way to minimize the pile deflection and bending moment is to improve the FBP soil around the excavation level. The FBP soil improvement 2—4 m below the pile head is not very useful for reducing the pile deflection and can be eliminated when the pile displacement limit is not very strict.
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    Mechanism Explanation of Influence of Dry Density and Water Content on Bentonite Swelling Process
    LI Xiaoyue1∗ (李晓月), ZHENG Xinjiang2 (郑新江)
    2024, 29 (5):  930-939.  doi: 10.1007/s12204-023-2668-x
    Abstract ( 16 )   PDF (1148KB) ( 6 )  
    The swelling process of bentonite is vital for judging the time required for completing the swelling, estimating the engineering safety, and organizing the construction plan. Many factors affect the swelling process, and the underlying mechanisms still require to be clearly explained. In this paper, the swelling process of commercial bentonite in different molar concentrations of salt solution was studied by the one-dimensional free swelling test and constant volume swelling pressure test. The curves of swelling over time were fitted using a hyperbolic model, and two parameters were extracted to reflect the swelling rate and the final swelling strain or swelling pressure quantitatively, respectively. The test results show that the final swelling strain or swelling pressure is determined by the swelling ability of the bentonite, while the swelling rate is influenced by the coupled effect of the swelling ability and permeability of soil. The mechanisms of different factors affecting the swelling process of bentonite are summarized as the effects on the permeability and swelling ability of the soil by considering the change process of pore structure during swelling. The proposed mechanism explanation can also reasonably explain the effect of initial water content in the existing literature. The influencing mechanism of the swelling process revealed in this paper from the perspective of pore structure provides a reasonable theoretical basis for analyzing the swelling process of bentonite.
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    Natural Vibration Characteristics for Prestressed Concrete-Filled Rectangular Steel Tube Simply Supported Beam
    YE Junxian (叶俊贤), HUANG Weixuan (黄维璇), LI Siping (李四平)
    2024, 29 (5):  940-944.  doi: 10.1007/s12204-023-2617-8
    Abstract ( 12 )   PDF (835KB) ( 7 )  
    The dynamic control equation of a new prestressed partially concrete-filled rectangular steel tube (CFRT) beam can be derived based on D’Alembert’s principle. It is used to infer the theoretical results of the dynamic characteristics for the prestressed CFRT beam. Additionally, the finite element model is set up by ABAQUS for simulation analysis. The results show that the natural vibration frequencies and mode function of the prestressed CFRT simply supported beam calculated by the theoretical formulas are reliable since the relative errors of the first-order frequencies under different prestressing levels are within 6% compared with the finite element results. Further analysis of the prestressing parameters is carried out using the theoretical formulas, in which factors such as the prestressing level, eccentricity of tendons, and tensile stiffness of prestressed tendons have different influences on the natural vibration frequencies. Finally, it provides a theoretical basis for the dynamic design of the prestressed CFRT beams.
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