Extending application of asymmetric semi-circular bend specimen to investigate mixed mode Ⅰ/Ⅱ fracture behavior of granite

The asymmetric semi-circular bend(ASCB)specimen has been proposed to investigate the cracking behavior in different geo and construction materials and attracted the attention of researchers due to its advantages.However,there are few studies on the fracture toughness determination of rock materials.In this work,a series of fracture tests were performed with the ASCB specimens made of granite.The onset of fracture,crack initiation angle and crack propagating trajectory was analyzed in detail combined with several mixed mode fracture criteria.The influence of the crack length on the mode Ⅰ/Ⅱ fracture toughness was studied.A comparison between the fracture toughness ratios predicted by varying criteria and experimental results was conducted.The relationship between experimentally determined crack initiation angles and curves of the generalized maximum tangential stress(GMTS)criterion was obtained.The fracture process of the specimen was recorded with the high-speed camera.The shortcomings of the ASCB specimens for the fracture toughness determination of rock materials were discussed.The results may provide a reference for analysis of mixed mode I and II fracture behavior of brittle materials.

Wave Forces on Submerged Semi-Circular Breakwater and Similar Structures

The results of design and experiment of a submerged semi-circular breakwater at the Yangtze estuary show that the submerged structure will be unsafe when the general empirical wave force formula for semi-circular breakwater is used in design. Therefore, a new calculation method for the wave forces acting on a submerged semi-circular structure is given in this paper, in which the wave force acting on the inside circumference of semi-circular arch is included, and the phase modification coefficient in the general empirical formula is adjusted as well. The new wave force calculation method has been Verified by the results of seven related physical model tests and adopted in the design of the south esturary jetty of the first stage project of Deep Channel Improvement Project of the Yangtze River Estuary, the total jetty length being 17.5 km.

Anti-plane (SH) waves diffraction by an underground semi-circular cavity:analytical solution

Diffraction of a two-dimensional （2D） semi-circular cavity in a half-space under incident SH-waves is studied using the classic wave function expansion method with a new de-coupling technique. This so-called ＂improved cosine half- range expansion＂ algorithm exhibits an excellent performance in reducing displacement residual errors at two rim points of concern. The governing equations are developed in a manner that minimizes the residues of the boundary conditions. Detailed derivation and analysis procedures as well as truncation of infinite linear governing equations are presented. The semi-circular cavity model presented in this paper, due to its simple profile, is expected to be used in seismic wave propagation studies as a benchmark for examining the accuracies of various analytical or numerical methods for mixed-boundary wave propagation problems.

Diffraction of plane SH waves by a semi-circular cavity in half-space

This paper presents a closed-form solution for diffraction of plane SH waves by a semi-circular cavity in half-space by using wave function expansion method. Accuracy of the solution is checked by the displacement residual and stress residual along the boundaries. Numerical results show that there are notable differences for response amplitudes between a semi-circular cavity and a whole-circular cavity in a half-space.

Study on the Interaction of Water Waves with Semi-Circular Breakwater

The present study investigates the interaction of steep waves with semi-circular breakwater with the complex plane's Cauchy boundary integral theorem. The boundary integral method is used to transform the calculation in fluid domain into its boundary alone. In the calculation the computation domain is moved with the propagation of waves. A numerical solution is obtained for incident Stokes waves passing the submerged obstacles. This method has been extended to the calculation of wave run-up on a slope for estimating wave overtopping.

The dispersion of particles in turbulent semi-circular duct flows

The flow field in a semi-circular duct is simulated by Large Eddy Simulation(LES)and its particle field is simulated by Lagrange particle tracking method.Reynolds number Reb(based on bulk velocity and hydraulic diameter)is 80,000 and Ret(based on friction velocity and hydraulic diameter)is 3528.Particle diameter dpis chosen as 10,50,100,500 mm corresponding to St as 0.10,2.43,9.72,243.05.The results show that the intensity of the secondary flow near the ceiling is less than that near the floor because the ceiling is curved and able to inhibit the secondary flow.It is found that the difference between the semicircular duct and the square duct is that the secondary flow in a corner of the semi-circular duct is not symmetrical along the diagonal although they have the same generation mechanism.Regarding the particles,small particles(dp≤10 mm)are found to uniformly distribute in the duct,while large particles(dp≥50 mm)preferentially distribute in the corner and floor center.The maximum particles(dp=500mm)fall on the floor quickly and their dispersion mainly depends on the secondary flow near the floor.Particle deposition in the corner depends on particle size due to the effect of secondary flow and gravity.The effect of lift force on particles becomes more significant for 50 and 100 mm particles in comparison with other smaller particles.In the end,the effect of secondary flow is found to be more significant to dominate particle behavior than that of flow fluctuation.

Determination of dynamic modeⅠfracture toughness of rock at ambient high temperatures using notched semi-circular bend method

To investigate the influence of loading rate and high temperature on the dynamic fracture toughness of rock,dynamic fracture tests were carried out on notched semi-circular bend specimens under four temperature conditions based on the split Hopkinson pressure bar system.Experimental and analytical methods were applied to investigating the effect of temperature gradient on the stress waves.A high-speed camera was used to check the fracture characteristics of the specimens.The results demonstrate that the temperature gradient on the bars will not significantly distort the shape of the stress wave.The dynamic force balance is achieved even when the specimens are at a temperature of 400°C.The dynamic fracture toughness linearly develops with the increase of loading rate within the temperature range of 25-400°C,and high temperature has a strengthening effect on the dynamic fracture toughness.

MODELING THE INTERACTION OF SOLITARY WAVES AND SEMI-CIRCULAR BREAKWATERS BY USING UNSTEADY REYNOLDS EQUATIONS

A vertical 2-D numerical wave model was developed based on unsteady Reynolds equations. In this model, the k-epsilon models were used to close the Reynolds equations, and volume of fluid(VOF) method was used to reconstruct the free surface. The model was verified by experimental data. Then the model was used to simulate solitary wave interaction with submerged, alternative submerged and emerged semi-circular breakwaters. The process of velocity field, pressure field and the wave surface near the breakwaters was obtained. It is found that when the semi-circular breakwater is submerged, a large vortex will be generated at the bottom of the lee side wall of the breakwater; when the still water depth is equal to the radius of the semi-circular breakwater, a pair of large vortices will be generated near the shoreward wall of the semi-circular breakwater due to wave impacting, but the velocity near the bottom of the lee side wall of the breakwater is always relatively small. When the semi-circular breakwater is emerged, and solitary wave cannot overtop it, the solitary wave surface will run up and down secondarily during reflecting from the breakwater. It can be further used to estate the diffusing and transportation of the contamination and transportation of suspended sediment.

A review on evaluation of crack resistance of asphalt mixture by semi-circular bending test

Although there are many kinds of fracture tests to choose from in evaluating the crack resistance of asphalt mixture,the semi-circular bending(SCB)test has attracted a lot of attention in the academic road engineering community because of its simplicity,stability,and flexibility in testing and evaluation.The SCB test has become a common method to study the cracking resistance of asphalt mixture in recent years.This paper mainly summarizes the overview of the SCB test,summarizes some research results and common characterization parameters of the SCB test method in monotone test and fatigue test in recent years,and predicts and suggests the research direction of the SCB test in the future.It is found that the research on the monotonic SCB test is more comprehensive,and the research on the SCB fatigue test needs to be further improved in the aspects of loading mode,characterization parameter selection,and so on.Researchers can flexibly adjust the geometric dimensions and the test parameters of semi-cylindrical specimens,and conduct comprehensive analysis combined with the results of numerical simulation.The crack resistance of asphalt mixture can be comprehensively evaluated by fracture energy,fracture toughness,stiffness,flexibility index and other fracture indicators,combined with the crack propagation of the specimen.The analysis of numerical simulation can confirm the test results.In order to standardize the setting of fatigue parameters for future application,it is necessary to standardize the setting of bending performance.

Asymmetric light propagation based on semi-circular photonic crystals

A new structure based on a semi-circular photonic crystal is proposed to achieve asymmetric light propagation. The semi-circular photonic crystal structure proposed in this paper is a deformation of a two-dimensional conventional square photonic crystal. Through the directional bandgap of the semi-circular photonic crystal, the light from one direction can transfer to the other side, but the light from the opposite direction cannot. A high contrast ratio is obtained by designing the constitutive parameters of the photonic crystal and choosing the suitable light frequency. This structure promises a significant potential in optical integration and other areas.

Simulation of Wave Forces on A Semi-Circular Breakwater Using Multilayer Feed Forward Network

In this paper, the Artificial Neural Network (ANN) is used to study the wave forces on a semi-circular breakwater. The process of establishing the network model for a specific physical problem is presented. Networks with double implicit layers have been studied by numerical experiments. 117 sets of experimental data are used to train and test the ANN. According to the results of ANN simulation, this method is proved to have good precision compared with experimental and numerical results.

Mixed convection in the heated semi-circular lid-driven cavity for non-Newtonian power-law fluids: Effect of presence and shape of the block

The present work delineates the hydrodynamics and thermal characteristics due to mixed convection in the liddriven semi-circular cavity affected by the presence of the adiabatic block at its geometric center for twodimensional,steady-state,laminar and for non-Newtonian power-law fluids.The semi-circular cavity has a diameter of D.The horizontal wall/lid is sliding with a uniform horizontal velocity(u=U)and is subjugated to the ambient thermal condition;while the curved surface is subjugated to a higher isothermal temperature.The convective characteristics inside the system is explored for the broad range of Richardson number(0.1≤Ri≤10),Prandtl number(1≤Pr≤100)and non-Newtonian power-law index(0.5≤n≤1.5)at a constant Grashof number of 10~4.Apart from this,the effect of shape(cross-section)of the inserted block,i.e.,circular,square and triangular on heat transfer characteristics has also been explored.It is observed that the shear thickening fluids display better cooling characteristics.Besides,the cavity with immersed triangular block shows better heat transfer results than the circular and square blocks.The deviations observed in the flow and heat transfer characteristics in the cavity by inserting an adiabatic block as compared with cavity without block have been ascertained by calculating normalized Nusselt number(Nu^N).The presence of the block was found to have a diminishing effect on the heat transfer due to convection in the cavity.In the end,the results of the study are summarized in the form of a predictive correlation exhibiting the functional dependence of average Nusselt number with Prandtl number,power-law index,and Richardson number.

Aeolian Tone from a Semi-Circular Cylinder in a Stream

Aeolian tone from a semi-circular cylinder in a uniform flow is studied experimentally for various angles of attack. It is found that the peak sound spectrum of the Aeolian tone from the semi-circular cylinder is smaller than that from the circular cylinder and the lowest sound is observed around the zero angle of attack. This is due to the reduction in the fluctuating lift force on the semi-circular cylinder compared to that of the circular cylinder. This result suggests the validity of the analogy between the sound pressure level and the fluctuating lift force on a semi-circular cylinder in a stream. The flow visualization study also supports these results.

Sound Source Measurement of a Semi-Circular Cylinder in a Uniform Flow by Particle Image Velocimetry

In this paper, the measurement of an aerodynamic sound source for a semi-circular cylinder in a uniform flow is described using Particle Image Velocimetry (PIV). This experimental technique is based on vortex sound theory, where the time derivative of vorticity is evaluated with the aid of two sets of standard PIV systems. The experimental results indicate that the sound source for the semi-circular cylinder is located around the shear layer near the edge of the semi-circular cylinder. The sound source intensity and the area are reduced in the semi-circular cylinder compared with those of a circular cylinder. This result indicates that the aerodynamic sound of the semi- circular cylinder is smaller than that of the circular cylinder, which supports the microphone measurement result.

Simulation of Natural Convection Flow with Magneto-Hydrodynamics in a Wavy Top Enclosure with a Semi-Circular Heater

Natural convection flow in enclosure has different applications such as room ventilation, heat exchangers, the cooling system of a building etc. The Finite-Element method based on the Galerkin weighted residual approach is used to solve two-dimensional governing mass, momentum and energy-equations for natural convection flow in the presence of a magnetic field on a roof top with semi-circular heater. In the enclosure the horizontal lower wall was heated, the vertical two walls were adiabatic, inside the semi-circular heater, the wavy top wall cooled. The parameters Rayleigh number, Hartmann number and Prandtl number are considered. The effects of the Hartmann number and Rayleigh number on the streamlines, isotherms, velocity profiles and average Nusselt number are examined graphically. The local Nusselt number and the average Nusselt number of the heated portion of the enclosure with the semi-circular heater are presented in this paper. Finally, for the validation of the existing work, the current results are compared with published results and the auspicious agreement is achieved.

Impacts of ice cover on local scour around semi-circular bridge abutment

The presence of ice cover in winter can significantly change the flow field around bridge abutments, which can also cause a different local scour pattern. To investigate the impacts of ice cover, results from a recent flume experiments were presented. Smooth and rough ice covers were created to investigate the impacts of ice cover roughness on the scour geometry around the semi-circular abutment. Three bed materials were used, with 50D s of 0.58 mm, 0.50 mm, 0.47 mm respectively. Scour volume and scour area were calculated. It was found that the maximum scour depth was located 75o inclined to the flume wall. Under rough ice cover, the scour area and scour depth were the largest. An empirical equation on the maximum scour depth was also developed.

DETERMINATION OF CRACK SURFACE DISPLACEMENTS FOR A RADIAL CRACK EMANATING FROM A SEMI-CIRCULAR NOTCH USING WEIGHT FUNCTION METHOD

A radial crack emanating from a semi-circular notch is of significant engineering importance. Accurate determination of key fracture mechanics parameters is essential for damage tolerance design and fatigue crack growth life predictions. The purpose of this paper is to provide an efficient and accurate closed-form weight function approach to the calculation of crack surface displacements for a radial crack emanating from a semi-circular notch in a semi-infinite plate. Results are presented for two load conditions： remote applied stress and uniform stress segment applied to crack surfaces. Based on a correction of stress intensity factor ratio, highly accurate analytical equations of crack surface displacements under the two load conditions are developed by fitting the data obtained with the weight function method. It is demonstrated that the Wu- Carlsson closed-form weight functions are very efficient, accurate and easy-to-use for calculating crack surface displacements for arbitrary load conditions. The method will facilitate fatigue crack closure and other fracture mechanics analyses where accurate crack surface displacements are required.

应力波作用下红砂岩复合动态断裂特征研究

为探究应力波作用下红砂岩的复合动态断裂特性,采用分离式霍普金森压杆和数字图像技术对带预制裂缝的半圆盘三点弯曲试样开展冲击加载实验,分析加载率、波长对红砂岩动态拉伸、断裂特征的影响。结果表明:①红砂岩试样加载率与动态抗拉强度、断裂韧度及破坏率均呈一次函数关系;断裂能随加载率增大而增长415.27%。②随着波长增加,动态抗拉强度增长742.14%,其中断裂能增长54.49%,但能量吸收率呈下降趋势;裂纹扩展平均速度增长4.09%,且首尾裂纹应变增长时间出现滞后现象;破坏率增长效应得到强化。③冲击速度8 m/s时试件主裂纹首尾监测点位的应变平均增加84.31%。

大掺量橡胶粉对沥青玛蹄脂碎石混合料低温性能的影响

为提高废旧轮胎的回收利用率,将轮胎粉碎加工成橡胶粉,采用等体积法替换石灰石集料,优化橡胶粉级配设计,制备聚酯纤维掺量0.4%和不同橡胶粉替代率(0、1.5%、2.0%、2.5%、3.0%、3.5%、4.0%)的沥青玛蹄脂碎石混合料(stone mastic asphalt, SMA)。基于马歇尔稳定度试验和半圆弯曲(semi-circular bending, SCB)试验,采用SCB试件的极限拉应力、断裂能、断裂韧性和断裂劲度综合分析了不同低温环境下橡胶粉对SMA-13沥青混合料抗裂性能的影响。结果表明:SMA-13沥青混合料的最佳沥青用量与橡胶粉掺量成正比,橡胶粉掺量的增加会提高混合料的弹性性能。与石灰岩沥青混合料相比,橡胶粉沥青混合料抗裂能力更加稳定和优异。当橡胶粉替换率为3%时,SMA-13沥青混合料抵抗变形能力最强,可显著提升其低温性能,为沥青路面材料组成设计提供了理论依据。

New Approach to Lightning Strike Risk Assessment of Wind Farm

In the past,lightning strike risk assessment of buildings mainly referred to the Protection against Lightning—Part 2:Risk Management(IEC 62305-2-2010)based on protection angle method.Lightning strike risk assessment of wind farms was conducted according to the Lightning Protection for Wind Energy System(IEC 61400-24-2019),which proposed the method of lightning strike risk assessment for wind turbine.In fact,the basic idea of the two is the same,that is,the source of the lightning strike wind turbine is transformed from the former S1-S4 to the latter N D-N DJ.According to the above method,wind farm was evaluated,and it has been proved that the practice can not achieve good results.After 2018,China has issued the Guide to Evaluation of Lightning Protection Technology in Buildings(T/GZLY 3-2022)and the Technical Specifications for Lightning Interception in Forest Areas(T/LYCY 4062-2024)based on semicircle protection,in which the source of risk defined by lightning point was closer to the reality,highly targeted and effective.Taking offshore wind farm as an example,this paper introduced a new method of establishing six evaluation indicators to determine the risk level according to the principle of compliance and the new protection technology of semi-circular method,which can be used as a reference for technical personnel.