This paper proposes an effective reliability design optimizationmethod for fail-safe topology optimization(FSTO)considering uncertainty based on the moving morphable bars method to establish the ideal balance between ...This paper proposes an effective reliability design optimizationmethod for fail-safe topology optimization(FSTO)considering uncertainty based on the moving morphable bars method to establish the ideal balance between cost and robustness,reliability and structural safety.To this end,a performancemeasure approach(PMA)-based doubleloop optimization algorithmis developed tominimize the relative volume percentage while achieving the reliability criterion.To ensure the compliance value of the worst failure case can better approximate the quantified design requirement,a p-norm constraint approach with correction parameter is introduced.Finally,the significance of accounting for uncertainty in the fail-safe design is illustrated by contrasting the findings of the proposed reliabilitybased topology optimization(RBTO)method with those of the deterministic design method in three typical examples.Monte Carlo simulation shows that the relative error of the reliability index of the optimized structure does not exceed 3%.展开更多
Experiments are performed in a wave flume to demonstrate the Bragg reflection of linear gravity waves by artificial bars. Three different artificial bars with rectangular, triangular and rectified cosinoidal shapes ar...Experiments are performed in a wave flume to demonstrate the Bragg reflection of linear gravity waves by artificial bars. Three different artificial bars with rectangular, triangular and rectified cosinoidal shapes are placed discretely on the seabed for measurement of the Bragg reflection. A series of experimental conditions including the number of bars, the periodic bar spacing, the water depth and various wave conditions are tested. Key parameters influencing the Bragg resonances are investigated. The experimental data are compared with the values from both theoretical and numerical models. Some key parameters have proved to be effective in describing the primary resonances. Predictive equations of the characteristics for the Bragg reflection are proposed in this paper.展开更多
Investigating the wave field near structures in coastal and offshore engineering is of increasing significance. In the present study, simulation is done of the wave profile and flow field for waves propagating over su...Investigating the wave field near structures in coastal and offshore engineering is of increasing significance. In the present study, simulation is done of the wave profile and flow field for waves propagating over submerged bars, using PLIC-VOF (Pieeewise Linear Interface Construction) to trace the free surface of wave and finite difference method to solve vertical 2D Navier-Stokes (N-S) equations. A comparison of the numerical results for two kinds of submerged bars with the experimental ones shows that the PLIC-VOF model used in this study is effective and can compute the wave field precisely.展开更多
The effect of freezing and thawing cycles on mechanical properties of concrete (compressive, splitting tensile strength) was experimentally investigated. According to the pullout test data of three kinds of deformed...The effect of freezing and thawing cycles on mechanical properties of concrete (compressive, splitting tensile strength) was experimentally investigated. According to the pullout test data of three kinds of deformed steel bars, the bond stress-slip curves after freezing and thawing were obtained. The empirical equations of peak bond strength were proposed that the damage accounted for effects of freezing and thawing cycle. Meanwhile, the mechanism of bond deterioration between steel bars and concrete after freezing and thawing cycles was discussed. All these conclusions will be useful to the durability design and reliability calculation of RC structures in cold region.展开更多
This paper examines the quasi-static cyclic behavior, lateral strength and equivalent damping capacities of a system of post-tensioned segmental bridge columns tied with large diameter martensitic Shape Memory Alloy ...This paper examines the quasi-static cyclic behavior, lateral strength and equivalent damping capacities of a system of post-tensioned segmental bridge columns tied with large diameter martensitic Shape Memory Alloy (SMA) link-bars. Moment-curvature constitutive relationships are formulated and analysis tools are developed for the PT column, including a modified four-spring model prepared for the SMA bars. The suggested system is exemplified using a column with an aspect ratio of 7.5 and twelve 36.5 mm diameter NiTi martensitic SMA bars. A post-tensioning force of 40% to 60% of the tendon yield strength is applied in order to obtain a self re-centering system, considering the residual stress of the martensitie SMA bars. The cyclic response results show that the lateral strength remains consistently around 10% of the total vertical load and the equivalent viscous damping ratios reach 10%-12% of critical. When large diameter NiTi superelastic SMA bars are incorporated into the column system, the cyclic response varies substantially. The creep behavior of the superelastic SMA bar is accounted for since it affects the re-centering capability of the column. Two examples are presented to emphasize the modeling sensitivities for these special bars and quantify their cyclic behavior effects within the column assembly.展开更多
To investigate the effect of different environmental conditions of GFRP bars in concrete beams with work cracks subjected to sustained loads, the beams were exposed in indoor, freeze/thaw cycles and immersed in alkali...To investigate the effect of different environmental conditions of GFRP bars in concrete beams with work cracks subjected to sustained loads, the beams were exposed in indoor, freeze/thaw cycles and immersed in alkaline solution at elevated temperature. The bars were carefully extracted from the beams and tested in order to evaluate residual tensile properties. The results show that the tensile strength decreased significantly in the highly aggressive conditions but not in the natural conditions. The effect of GFRP bars casting in concrete beams demonstrated approximately 2.5% decrease of tensile strength caused by pore water environment in concrete beams on basis of those of the original bars. The effect of sustained loading plus work cracks demonstrated about 10.5% tensile strength decrease on basis of those of the bars only casted in concrete beams. The effect of environments under sustained loading plus work cracks demonstrated about 17% tensile strength decrease caused by a saturated solution of Ca(OH)2 and 60-2 ℃ tap water (pH=12-13) and about 8% tensile strength decrease caused by freezing and thawing cycle (F/T), both on basis of those of the bars of the indoor beams only under sustained loading plus work cracks. The results demonstrate the effects of the tensile strengths under different environmental conditions of GFRP bars in concrete beams with work cracks subjected to sustained loads.展开更多
Wave decomposition phenomenon and spectrum evolution over submerged bars are investigated by a previously developed numerical model. First, the computed free surface displacements of regular waves at various locations...Wave decomposition phenomenon and spectrum evolution over submerged bars are investigated by a previously developed numerical model. First, the computed free surface displacements of regular waves at various locations are compared with the available experimental data to confirm the validity of the numerical model, and satisfactory agreements are obtained. In addition, variations of decomposition characteristics with incident wave parameters and the change of energy spectrum for regular waves are also studied. Then the spectrum evolution of irregular waves over submerged bars, as well as the influence of incident peak wave period and the steepness of the front slope of the bar on spectrum evolution, is investigated. Wave decomposition and spectral shape are found to be significantly influenced by the incident wave conditions. When the upslope of the bar becomes 1:2, the length of the slope becomes shorter and will not benefit the generation of high frequency energy, so spectrum evolution is not significant.展开更多
To improve corrosion-resistance of shallow-buried concrete urban utility tunnels(UUTs),basalt fiber reinforced polymer(BFRP)bars are applied to reinforce UUTs.As the UUT must have excellent survival capability under a...To improve corrosion-resistance of shallow-buried concrete urban utility tunnels(UUTs),basalt fiber reinforced polymer(BFRP)bars are applied to reinforce UUTs.As the UUT must have excellent survival capability under accidental explosions,a shallow-buried BFRP bars reinforced UUT(BBRU)was designed and constructed.Repetitive blast experiments were carried out on this BBRU.Dynamic responses,damage evolutions and failure styles of the BBRU under repetitive explosions were revealed.The tunnel roof is the most vulnerable component and longitudinal cracks develop along the tunnel.When the scaled distance is larger than 1.10 m/kg1/3,no cracks are observed in the experiments.When the BBRU is severely damaged,there are five cracks forming and developing along the roof.The roof is simplified as a clamped-supported one-way slab,proved by the observation that the maximum strain of the transverse bar is much larger than that of the longitudinal bar.Dynamic responses of the roof slab are predicted by dynamic Euler beam theory,which can consistently predict the roof displacement under large-scaleddistance explosion.Compared with the UUT reinforced with steel bars,the BBRU has advantages in blast resistance with smaller deflections and more evenly-distributed cracks when the scaled distance is smaller than 1.260 m/kg1/3 and the steel bars enter plastic state.Longer elastic defamation of the BFRP bars endows the UUT more excellent blast resistance under small-scaled-distance explosions.展开更多
InGaSb/AlGaAsSb double-quantum-well diode lasers emitting around 2 μm are demonstrated. The AlGaAsSb barriers of the lasers are grown with digital alloy techniques consisting of binary AlSb/AlAs/GaSb short-period pai...InGaSb/AlGaAsSb double-quantum-well diode lasers emitting around 2 μm are demonstrated. The AlGaAsSb barriers of the lasers are grown with digital alloy techniques consisting of binary AlSb/AlAs/GaSb short-period pairs. Peak power conversion efficiency of 26% and an efficiency higher than 16% at 1 W are achieved at continuous-wave operation for a 2-mm-long and 100-μm-wide stripe laser. The maximum output power of a single emitter reaches to 1.4 W at 7 A.19-emitter bars with maximum efficiency higher than 20% and maximum power of 16 W are fabricated. Lasers with the short-period-pair barriers are proved to have improved temperature properties and wavelength stabilities. The characteristic temperature(T_0) is up to 140?C near room temperature(25–55?C).展开更多
Ductile iron bars(DIBs) with a diameter of 145 mm, used for plunger pump production, were made by the horizontal continuous casting(HCC). The microstructure of the samples cut at three locations with different distanc...Ductile iron bars(DIBs) with a diameter of 145 mm, used for plunger pump production, were made by the horizontal continuous casting(HCC). The microstructure of the samples cut at three locations with different distances away from the surface(~20 mm from the surface, half of the radius and the center of the HCCDIBs)were investigated. The mechanical properties were measured by tensile and torsion tests. Results show that after the spheroidization of graphite, the iron matrix incorporates the nodules of Format I, Size 8 close to the surface, Format I, Size 7 at the half of the radius from the surface, and Format II, Size 6 in the centre of the bar,according to the ASTM A247 standard. The content of pearlite in the matrix changes from 55%(~20 mm from the surface) to 70%(half of the radius) and 80%(the center of the HCCDIBs). The strengths in tension are 552, 607 and 486 MPa with the elongations of 12.5%, 10.5% and 5.8% in samples cut at these three locations from the surface to the centre, respectively. The strength in torsion is equal to 558, 551 and 471 MPa at corresponding torsion angles of 418°, 384° and 144° respectively to the same distance from the bar surface. Fracture in tension is manifested via crack propagation through the interface between graphite nodules and matrix(Mode I), while in torsion the fracture is caused by the shear of graphite nodules(Mode II). It is shown that the transition between two fracture modes is also dependent on the size of graphite nodule. Typically, fracture Mode I was observed for nodules of smaller diameter(less than 22.7 μm) and fracture Mode II was seen for nodules of greater diameter(more than 24.8 μm).展开更多
This study examines oblique wave motion over multiple submerged porous bars in front of a vertical wall. Based on linear potential theory, an analytical solution for the present problem is developed using matched eige...This study examines oblique wave motion over multiple submerged porous bars in front of a vertical wall. Based on linear potential theory, an analytical solution for the present problem is developed using matched eigenfunction expansions. A complex dispersion relation is adopted to describe the wave elevation and energy dissipation over submerged porous bars. In the analytical solution, no limitations on the bar number, bar size, and spacing between adjacent bars are set. The convergence of the analytical solution is satisfactory, and the correctness of the analytical solution is confirmed by an independently developed multi-domain BEM (boundary element method) solution. Numerical examples are presented to examine the reflection and transmission coefficients of porous bars, CR and Cv, respectively, for engineering applications. The calculation results show that when the sum of widths for all the porous bars is fixed, increasing the bar number can significantly improve the sheltering function of the bars. Increasing the bar height can cause more wave energy dissipation and lower CR and Cr. The spacing between adjacent bars and the spacing between the last bar and the vertical wall are the key parameters affecting CR and Ct. The proposed analytical method may be used to analyze the hydrodynamic performance of submerged porous bars in preliminary engineering designs.展开更多
Nine PHC piles with partial normal-strength deformed bars were prepared in present study,and cyclic loading tests were implemented to evaluate these piles’seismic performance.The influence of the axial compression ra...Nine PHC piles with partial normal-strength deformed bars were prepared in present study,and cyclic loading tests were implemented to evaluate these piles’seismic performance.The influence of the axial compression ratio and the amount of normal-strength deformed bars on failure modes,crack patterns,strength,stiffness,and ductility were examined.The test findings indicate that the change of axial compression ratio has a noticeable influence on the failure mode of PHC piles.A larger axial compression ratio results in a higher cracking bending resistance,ultimate bending resistance,and initial stiffness,but the propagation heights of flexural cracks decrease as the axial compression ratio increases.Furthermore,increasing the amount of normal-strength deformed bars causes a slight decrease in ductility.Finally,a calculation formula was proposed to predict the flexural capacity of PHC piles with partial normal-strength deformed bars.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12172114)Natural Science Foundation of Anhui Province(Grant No.2008085QA21)+1 种基金Fundamental Research Funds for the Central Universities(Grant No.JZ2022HGTB0291)China Postdoctoral Science Foundation(Grant No.2022M712358).
文摘This paper proposes an effective reliability design optimizationmethod for fail-safe topology optimization(FSTO)considering uncertainty based on the moving morphable bars method to establish the ideal balance between cost and robustness,reliability and structural safety.To this end,a performancemeasure approach(PMA)-based doubleloop optimization algorithmis developed tominimize the relative volume percentage while achieving the reliability criterion.To ensure the compliance value of the worst failure case can better approximate the quantified design requirement,a p-norm constraint approach with correction parameter is introduced.Finally,the significance of accounting for uncertainty in the fail-safe design is illustrated by contrasting the findings of the proposed reliabilitybased topology optimization(RBTO)method with those of the deterministic design method in three typical examples.Monte Carlo simulation shows that the relative error of the reliability index of the optimized structure does not exceed 3%.
基金by the National Science Council of Taiwan under the contract number of NSC87-2611-E-006-019
文摘Experiments are performed in a wave flume to demonstrate the Bragg reflection of linear gravity waves by artificial bars. Three different artificial bars with rectangular, triangular and rectified cosinoidal shapes are placed discretely on the seabed for measurement of the Bragg reflection. A series of experimental conditions including the number of bars, the periodic bar spacing, the water depth and various wave conditions are tested. Key parameters influencing the Bragg resonances are investigated. The experimental data are compared with the values from both theoretical and numerical models. Some key parameters have proved to be effective in describing the primary resonances. Predictive equations of the characteristics for the Bragg reflection are proposed in this paper.
文摘Investigating the wave field near structures in coastal and offshore engineering is of increasing significance. In the present study, simulation is done of the wave profile and flow field for waves propagating over submerged bars, using PLIC-VOF (Pieeewise Linear Interface Construction) to trace the free surface of wave and finite difference method to solve vertical 2D Navier-Stokes (N-S) equations. A comparison of the numerical results for two kinds of submerged bars with the experimental ones shows that the PLIC-VOF model used in this study is effective and can compute the wave field precisely.
基金the National Natural Science Foundation of China(No.50479059)
文摘The effect of freezing and thawing cycles on mechanical properties of concrete (compressive, splitting tensile strength) was experimentally investigated. According to the pullout test data of three kinds of deformed steel bars, the bond stress-slip curves after freezing and thawing were obtained. The empirical equations of peak bond strength were proposed that the damage accounted for effects of freezing and thawing cycle. Meanwhile, the mechanism of bond deterioration between steel bars and concrete after freezing and thawing cycles was discussed. All these conclusions will be useful to the durability design and reliability calculation of RC structures in cold region.
基金Research fund of Hanyang University Under Grant No.HY-2010-N
文摘This paper examines the quasi-static cyclic behavior, lateral strength and equivalent damping capacities of a system of post-tensioned segmental bridge columns tied with large diameter martensitic Shape Memory Alloy (SMA) link-bars. Moment-curvature constitutive relationships are formulated and analysis tools are developed for the PT column, including a modified four-spring model prepared for the SMA bars. The suggested system is exemplified using a column with an aspect ratio of 7.5 and twelve 36.5 mm diameter NiTi martensitic SMA bars. A post-tensioning force of 40% to 60% of the tendon yield strength is applied in order to obtain a self re-centering system, considering the residual stress of the martensitie SMA bars. The cyclic response results show that the lateral strength remains consistently around 10% of the total vertical load and the equivalent viscous damping ratios reach 10%-12% of critical. When large diameter NiTi superelastic SMA bars are incorporated into the column system, the cyclic response varies substantially. The creep behavior of the superelastic SMA bar is accounted for since it affects the re-centering capability of the column. Two examples are presented to emphasize the modeling sensitivities for these special bars and quantify their cyclic behavior effects within the column assembly.
基金Funded Partly by the National Natural Science Foundation of China(No.51178361)
文摘To investigate the effect of different environmental conditions of GFRP bars in concrete beams with work cracks subjected to sustained loads, the beams were exposed in indoor, freeze/thaw cycles and immersed in alkaline solution at elevated temperature. The bars were carefully extracted from the beams and tested in order to evaluate residual tensile properties. The results show that the tensile strength decreased significantly in the highly aggressive conditions but not in the natural conditions. The effect of GFRP bars casting in concrete beams demonstrated approximately 2.5% decrease of tensile strength caused by pore water environment in concrete beams on basis of those of the original bars. The effect of sustained loading plus work cracks demonstrated about 10.5% tensile strength decrease on basis of those of the bars only casted in concrete beams. The effect of environments under sustained loading plus work cracks demonstrated about 17% tensile strength decrease caused by a saturated solution of Ca(OH)2 and 60-2 ℃ tap water (pH=12-13) and about 8% tensile strength decrease caused by freezing and thawing cycle (F/T), both on basis of those of the bars of the indoor beams only under sustained loading plus work cracks. The results demonstrate the effects of the tensile strengths under different environmental conditions of GFRP bars in concrete beams with work cracks subjected to sustained loads.
基金The National Natural Science Foundation of China for Distinguished Young Scholars under contract No. 50025925the Chinese Postdoctoral Science Foundation under contract No. 20040350088
文摘Wave decomposition phenomenon and spectrum evolution over submerged bars are investigated by a previously developed numerical model. First, the computed free surface displacements of regular waves at various locations are compared with the available experimental data to confirm the validity of the numerical model, and satisfactory agreements are obtained. In addition, variations of decomposition characteristics with incident wave parameters and the change of energy spectrum for regular waves are also studied. Then the spectrum evolution of irregular waves over submerged bars, as well as the influence of incident peak wave period and the steepness of the front slope of the bar on spectrum evolution, is investigated. Wave decomposition and spectral shape are found to be significantly influenced by the incident wave conditions. When the upslope of the bar becomes 1:2, the length of the slope becomes shorter and will not benefit the generation of high frequency energy, so spectrum evolution is not significant.
基金Supports from National Natural Science Foundation of China(51778622,11672130,and 11972184)Social Development Project of Science and Technology Department of Jiangsu Province(BE2017780)+1 种基金State Key Laboratory for Disaster Reduction in Civil Engineering(SLDRCE16-01)State Key Laboratory of Mechanics and Control of Mechanical Structures(MCMS-0217G03)are gratefully acknowledged.
文摘To improve corrosion-resistance of shallow-buried concrete urban utility tunnels(UUTs),basalt fiber reinforced polymer(BFRP)bars are applied to reinforce UUTs.As the UUT must have excellent survival capability under accidental explosions,a shallow-buried BFRP bars reinforced UUT(BBRU)was designed and constructed.Repetitive blast experiments were carried out on this BBRU.Dynamic responses,damage evolutions and failure styles of the BBRU under repetitive explosions were revealed.The tunnel roof is the most vulnerable component and longitudinal cracks develop along the tunnel.When the scaled distance is larger than 1.10 m/kg1/3,no cracks are observed in the experiments.When the BBRU is severely damaged,there are five cracks forming and developing along the roof.The roof is simplified as a clamped-supported one-way slab,proved by the observation that the maximum strain of the transverse bar is much larger than that of the longitudinal bar.Dynamic responses of the roof slab are predicted by dynamic Euler beam theory,which can consistently predict the roof displacement under large-scaleddistance explosion.Compared with the UUT reinforced with steel bars,the BBRU has advantages in blast resistance with smaller deflections and more evenly-distributed cracks when the scaled distance is smaller than 1.260 m/kg1/3 and the steel bars enter plastic state.Longer elastic defamation of the BFRP bars endows the UUT more excellent blast resistance under small-scaled-distance explosions.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61790580 and 61435012)the National Basic Research Program of China(Grant No.2014CB643903)the Scientific Instrument Developing Project of the Chinese Academy of Sciences(Grant No.YJKYYQ20170032)
文摘InGaSb/AlGaAsSb double-quantum-well diode lasers emitting around 2 μm are demonstrated. The AlGaAsSb barriers of the lasers are grown with digital alloy techniques consisting of binary AlSb/AlAs/GaSb short-period pairs. Peak power conversion efficiency of 26% and an efficiency higher than 16% at 1 W are achieved at continuous-wave operation for a 2-mm-long and 100-μm-wide stripe laser. The maximum output power of a single emitter reaches to 1.4 W at 7 A.19-emitter bars with maximum efficiency higher than 20% and maximum power of 16 W are fabricated. Lasers with the short-period-pair barriers are proved to have improved temperature properties and wavelength stabilities. The characteristic temperature(T_0) is up to 140?C near room temperature(25–55?C).
基金financially supported by the Shaanxi Provincial Science and Technology Achievement Transfer and Promotion Plan-absorb Achievement Transformation Project(No.2017CGZH-XNGJ-03)Shaanxi Provincial Education Department Scientific Research Program Project-service Local Special Industrialization Cultivation Project(No.17JF018)+1 种基金Xi'an Science and Technology Planning Project Science and Technology Innovation Guide Projects(No.201805037YD15CG21(19))Xi'an University of Technology Scientific and Technological Achievement Transformation Project-technical Requirement Solving Project of Enterprises(No.2018-1)
文摘Ductile iron bars(DIBs) with a diameter of 145 mm, used for plunger pump production, were made by the horizontal continuous casting(HCC). The microstructure of the samples cut at three locations with different distances away from the surface(~20 mm from the surface, half of the radius and the center of the HCCDIBs)were investigated. The mechanical properties were measured by tensile and torsion tests. Results show that after the spheroidization of graphite, the iron matrix incorporates the nodules of Format I, Size 8 close to the surface, Format I, Size 7 at the half of the radius from the surface, and Format II, Size 6 in the centre of the bar,according to the ASTM A247 standard. The content of pearlite in the matrix changes from 55%(~20 mm from the surface) to 70%(half of the radius) and 80%(the center of the HCCDIBs). The strengths in tension are 552, 607 and 486 MPa with the elongations of 12.5%, 10.5% and 5.8% in samples cut at these three locations from the surface to the centre, respectively. The strength in torsion is equal to 558, 551 and 471 MPa at corresponding torsion angles of 418°, 384° and 144° respectively to the same distance from the bar surface. Fracture in tension is manifested via crack propagation through the interface between graphite nodules and matrix(Mode I), while in torsion the fracture is caused by the shear of graphite nodules(Mode II). It is shown that the transition between two fracture modes is also dependent on the size of graphite nodule. Typically, fracture Mode I was observed for nodules of smaller diameter(less than 22.7 μm) and fracture Mode II was seen for nodules of greater diameter(more than 24.8 μm).
基金supported by the National Natural Science Foundation of China(Nos.51490675,51322903 and 51279224.)
文摘This study examines oblique wave motion over multiple submerged porous bars in front of a vertical wall. Based on linear potential theory, an analytical solution for the present problem is developed using matched eigenfunction expansions. A complex dispersion relation is adopted to describe the wave elevation and energy dissipation over submerged porous bars. In the analytical solution, no limitations on the bar number, bar size, and spacing between adjacent bars are set. The convergence of the analytical solution is satisfactory, and the correctness of the analytical solution is confirmed by an independently developed multi-domain BEM (boundary element method) solution. Numerical examples are presented to examine the reflection and transmission coefficients of porous bars, CR and Cv, respectively, for engineering applications. The calculation results show that when the sum of widths for all the porous bars is fixed, increasing the bar number can significantly improve the sheltering function of the bars. Increasing the bar height can cause more wave energy dissipation and lower CR and Cr. The spacing between adjacent bars and the spacing between the last bar and the vertical wall are the key parameters affecting CR and Ct. The proposed analytical method may be used to analyze the hydrodynamic performance of submerged porous bars in preliminary engineering designs.
基金National Natural Science Foundation of China under Grant No.51578369the Tianjin Science and Technology Major Project under Grant No.17ZXCXSF00080。
文摘Nine PHC piles with partial normal-strength deformed bars were prepared in present study,and cyclic loading tests were implemented to evaluate these piles’seismic performance.The influence of the axial compression ratio and the amount of normal-strength deformed bars on failure modes,crack patterns,strength,stiffness,and ductility were examined.The test findings indicate that the change of axial compression ratio has a noticeable influence on the failure mode of PHC piles.A larger axial compression ratio results in a higher cracking bending resistance,ultimate bending resistance,and initial stiffness,but the propagation heights of flexural cracks decrease as the axial compression ratio increases.Furthermore,increasing the amount of normal-strength deformed bars causes a slight decrease in ductility.Finally,a calculation formula was proposed to predict the flexural capacity of PHC piles with partial normal-strength deformed bars.