CN105825030A - Method for evaluating fatigue life of aged reinforced concrete bridge - Google Patents

Method for evaluating fatigue life of aged reinforced concrete bridge Download PDF

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CN105825030A
CN105825030A CN201610204595.1A CN201610204595A CN105825030A CN 105825030 A CN105825030 A CN 105825030A CN 201610204595 A CN201610204595 A CN 201610204595A CN 105825030 A CN105825030 A CN 105825030A
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马亚飞
郭忠照
张建仁
王磊
刘永明
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Changsha University of Science and Technology
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Abstract

The invention discloses a method for evaluating the fatigue life of an aged reinforced concrete bridge. The method comprises the following steps of obtaining initial corrosion time of reinforcement in concrete based on the second diffusion law of Fick, and considering the influence of concrete cracking due to corrosion expansion in a corrosion rate model; adopting a small crack growth and near threshold growth analysis and determining relevant parameters of fatigue crack propagation rate of materials by developing a fatigue crack propagation test of reinforced concrete materials; performing a corrosion fatigue test or finite element analysis on corroded reinforcement to obtain stress concentration factors at different corrosion levels, and integrating into a stress intensity factor model to obtain the fatigue crack propagation rate of the reinforcement under the influence of corrosion; comparing the magnitude of a corrosion pit growth rate and the fatigue crack propagation rate and gradually converting into a single growth analysis on fatigue cracks of the reinforcement; meanwhile, combining with vehicle load observing information to realize life evaluation of a bridge at different service stages. The prediction method disclosed by the invention is reasonable and high in popularization, and can provide technical support for evaluating the life of the concrete bridges.

Description

Aged reinforced concrete-bridge fatigue lifetime estimation method
Technical field
The present invention relates to treatment rates security evaluation field, particularly to a kind of aged reinforced concrete-bridge fatigue lifetime estimation method.
Background technology
Reinforced Concrete Bridge under arms during constantly bear Vehicle Load repeatedly.Meanwhile, under deicer salts or the environment such as coastal, in bridge, reinforcing bar easily corrodes.Reinforcement corrosion can accelerate fatigue accumulated damage, significantly reduces structure service life.Along with structural design theory progressively to making full use of the transformation of strength of materials aspect, the most growing volume of traffic and the impact of overload, the stress amplitude suffered by Reinforced Concrete Bridge can be increasing, occurs the probability of fatigue damage to be greatly improved.There are some researches show that the reduction of eroded reinforced concrete beam fatigue life is mainly reduced by steel area and fatigue strength is degenerated and caused, the impact of negligible Bond Degradation, fatigue failure all shows as the brittle break of reinforcing bar fatigue fracture.Therefore, can be using tension reinforcement as study subject.
Fatigue surplus life prediction at present is main uses two kinds of methods, and a kind of is that another kind is the analytic process based on fracture mechanics and crack growth based on material fatigue life curve and the analytic process of damage accumulation rule.Use linear damage accumulated damage method to calculate simplicity, but relatively large deviation may be produced under random load, it is difficult to as the single standard of Fatigue Life Assessment.Mostly analysis method based on Theory of Fracture Mechanics is to be analyzed based on the growth of long crack under uniaxial loading, and this method is mainly applied to pure analysis of fatigue by existing research, and does not considers infection；Another essential condition of the method is to obtain initial crack, and is limited by objective condition such as quality of materials, construction level and body structure surface are unsmooth, and accurately detection initial crack is brought the biggest difficulty.
Summary of the invention
For solving above-mentioned technical problem, the technical scheme is that,
A kind of aged reinforced concrete-bridge fatigue lifetime estimation method, comprises the following steps:
Step one: based on Fick the second diffusion law, calculates concrete reinforcing steel surface chlorine ion concentration and reaches the time of marginal value, i.e. obtain corrosion initial time；
Step 2: use corrosion electric current density to represent steel bar corrosion speed, calculates the crack time and ftractures to the critical width time, obtaining considering the steel bar corrosion rate calculations model that rust distending splits impact；Fatigue of materials crack growth rate relevant parameter is determined by carrying out the fatigue crack propagation test of bar material, carry out corrosion reinforcing bar fatigue test or finite element analysis obtain under different erosion levels fatiguestrength reduction factor and be dissolved in stress intensity factor model, obtain reinforcing bar fatigue crack growth rate under the influence of corrosion, relatively rust hole rate of rise and fatigue crack growth rate size, obtain crack growth rate cheat with rust rate of rise equal time elapsed time；
Step 3: analyzed by reinforcing bar fatigue crack growth, to fatigue crack growth model from equivalence initial crack size to critical crack length integration, obtain the load periodicity occurring fatigue fracture to be experienced, in conjunction with measured load frequency, and then obtain the reinforcing bar crack Propagation control time.
Described method, described step one includes:
Based on Fick the second diffusion law, rebar surface chlorine ion concentration is reached the time of criticality chlorine ion concentration as corrosion initial time, corrode initial time TiIt is expressed as
In formula: TiFor reinforcement corrosion initial time；DcFor diffusion coefficient；C0For concrete surface chlorine ion concentration；Erf is error function；C is protective layer thickness；CcrFor criticality chlorine ion concentration.
Described method, described step 2 includes,
After t, the local erosion depth spot on concrete reinforcing steel surface is
P (t)=0.0116R ∫ icorr(t)dt(2)
In formula: p (t) is the rust hole degree of depth；R is corrosion nonuniformity coefficient；icorrT () is electric current density；T is the time；Corrosion starts t after current density
icorr(t)=32.1 (1-w/c)-1.64·(t-Ti)-0.29/C(3)
In formula: w/c is the ratio of mud；
It is simultaneously introduced accelerator coefficient kacConsider the crack impact on corrosion rate,
In formula: Tsp,limFor swollen crack and damage time of becoming rusty, Tsp,lim=Ti+Tcr+Tcc；TcrStart to cracking time for corrosion；TccFor cracking to boundary spaced time, wherein,
In formula: d0For gap thickness around reinforcing bar；D is bar diameter；υ is Poisson's ratio；ψ=(D+2d0)2/2C(C+D+2d0)；ftFor concrete tensile strength；EefFor concrete effective modulus of elasticity, Eef=Ec/(1+φcr)；EcFor modulus of elasticity of concrete；φcrFor creep coefficient；fcFor concrete strength；
In formula: WlimFor boundary width；
Rebar surface rust hole rate of rise is
Equivalence initial crack is expressed as
In formula: aiFor equivalence initial crack size；ΔKthFor critical stress intensity factors, in Fatigue Crack Growth Rate figure 10-10The value that m/ week is corresponding；ΔσfFor fatigue limit；Y is the Geometric corrections factor；Wherein Geometric corrections factor Y is expressed as
Y=G (0.752+1.286 β+0.37 ω3)(9)
In formula:ω=1-sin β；A is crack length；
Carrying out fatigue crack growth rate test, reinforcing bar Fatigue Crack Growth Rate is expressed as
Da/dN=C (Δ K-Δ Kth)m(10)
In formula: C, m are and material relevant parameter that the crack growth rate drawn by material crack way of extensive experimentation-stress intensive factor range curve matching obtains；N is fatigue life cycle；Δ K is stress intensive factor range,Δ σ is stress amplitude, Δ σ=σmax-σmin, reinforcement stresses size is calculated by finite element modelling or " Code for design of concrete structures GB50010-2010 " and obtains；Calculate the stress intensity factor under infection, on the basis of fatigue crack growth rate is tested, the impact that rust hole causes stress to concentrate is quantified, use following formula to calculate rust hole Root Stress intensity factor Kp(t), wherein, KtFor fatiguestrength reduction factor；
Fatiguestrength reduction factor uses Finite Element Method by reality rust hole size Modeling Calculation or to simplify calculating as the following formula
A plastic correcting factor is used to reflect the plastic deformation of material, i.e.
In formula: ρ is Hookean region size；σ0For material static(al) hot strength；
Consider the stress intensity amplitude of plastic correctingA' is the crack length considering plastic correcting, i.e. a'=a+ ρ；
Rust hole Root Stress intensity factor is introduced in fatigue crack growth rate is tested, obtains considering the fatigue crack growth rate model of corrosion impact, by the function that this model conversation is time t
Da/dt=C (Δ Kp(t)-ΔKth)mf(14)
In formula: f is repeatedly the frequency of vehicular load；
Along with being continuously increased of load, there is a time point TtrSo that rust hole rate of rise is equal with crack growth rate, i.e.
Described method, described step 3 includes,
By crackle model of growth is realized last life appraisal from equivalence initial crack size to critical crack length integration
In formula: acCrack critical length corresponding during for losing efficacy, fracture toughness and imposed load by material obtain, and according to vehicular load frequency f of bridge actual measurement, fatigue load number N are scaled time Tcp。
Described method, life appraisal includes three phases: steel bar corrosion initial time Ti, reinforcing bar rust hole increase control time TtrTime T is controlled with reinforcing bar crack Propagationcp。
The method have technical effect that, use the theoretical analysis method combined with test, and incorporate real bridge vehicle load information, can effectively consider that reinforcement corrosion form, rust distending split, stress is concentrated, the competition of pitting corrosion rate of rise and crack growth rate, Forecasting Methodology is reasonable, generalization is strong, can be that the life appraisal of military service concrete-bridge provides technical support.
Accompanying drawing explanation
Fig. 1 is the Fatigue Life Assessment overall schematic of the present invention.
Fig. 2 is fatigue of materials crack growth rate relevant parameter matching schematic diagram.
Fig. 3 competes schematic diagram for rust hole rate of rise with fatigue crack growth rate.
Fig. 4 is the calculation flow chart of invention.
Detailed description of the invention
As it is shown in figure 1, life appraisal can be divided into three phases: steel bar corrosion initial time Ti, reinforcing bar rust hole increase control time Ttr, reinforcing bar crack Propagation control time Tcp.Specifically including step is:
(1) reinforcement corrosion initial time is determined
Based on Fick the second diffusion law, the time that rebar surface chlorine ion concentration reaches criticality chlorine ion concentration is represented by as corrosion initial time, corrosion initial time
In formula: TiFor reinforcement corrosion initial time；DcFor diffusion coefficient；C0For concrete surface chlorine ion concentration；Erf is error function；C is protective layer thickness；CcrFor criticality chlorine ion concentration.
(2) reinforcement corrosion speed size is determined
After t, the local erosion depth spot on concrete reinforcing steel surface is
P (t)=0.0116R ∫ icorr(t)dt(2)
In formula: p (t) is the rust hole degree of depth；R is corrosion nonuniformity coefficient；icorrT () is electric current density；T is the time.
The corrosion product of rebar surface attachment can produce impact to iron ion, causes corrosion electric current density to be gradually reduced with the growth of etching time.Therefore, corrosion beginning t after current density is
icorr(t)=32.1 (1-w/c)-1.64·(t-Ti)-0.29/C(3)
In formula: w/c is the ratio of mud.
After crack, corrosion rate is had certain impact.By introducing an accelerator coefficient kacConsider the cracking impact on corrosion rate,
In formula: Tsp,limFor swollen crack and damage time of becoming rusty, Tsp,lim=Ti+Tcr+Tcc；TcrStart to cracking time for corrosion；TccFor cracking to boundary spaced time.Wherein,
In formula: d0For gap thickness around reinforcing bar；D is bar diameter；υ is Poisson's ratio；ψ=(D+2d0)2/2C(C+D+2d0)；ftFor concrete tensile strength；EefFor concrete effective modulus of elasticity, Eef=Ec/(1+φcr)；EcFor modulus of elasticity of concrete；φcrFor creep coefficient；fcFor concrete strength.
In formula: WlimFor boundary width.
Rebar surface rust hole rate of rise is
(3) equivalence initial crack size is determined
Equivalence initial crack size non-real crack size, but a kind of equivalence long crack Analysis in Growth used to promote fatigue life prediction, equivalence initial crack is represented by
In formula: aiFor equivalence initial crack size；ΔKthFor critical stress intensity factors, in Fatigue Crack Growth Rate figure 10-10The value that m/ week is corresponding；ΔσfFor fatigue limit；Y is the Geometric corrections factor.
Circular reinforcing bar is under axial tension effect, and crackle crosswisely develops along cross section, and the Geometric corrections factor is represented by
Y=G (0.752+1.286 β+0.37 ω3)(9)
In formula:ω=1-sin β；
(4) fatigue crack growth rate test is carried out
Reinforcing bar Fatigue Crack Growth Rate is represented by
Da/dN=C (Δ K-Δ Kth)m(10)
In formula: C, m are and material relevant parameter that the crack growth rate can drawn by material crack expanding test-stress intensive factor range curve matching obtains (as shown in Figure 2)；N is fatigue life cycle；Δ K is stress intensive factor range,Δ σ is stress amplitude, Δ σ=σmax-σmin, the big I of reinforcement stresses is calculated by finite element modelling or " Code for design of concrete structures GB50010-2010 " and obtains.
(5) stress intensity factor under infection
On the basis of step (4), the impact that rust hole causes stress to concentrate is quantified, use following formula to calculate rust hole Root Stress intensity factor, wherein, KtFor fatiguestrength reduction factor.
Fatiguestrength reduction factor uses Finite Element Method by reality rust hole size Modeling Calculation or to simplify calculating as the following formula
In formula: D is bar diameter.
In high cycle fatigue analysis, can be assumed that material is elastic.For low-cycle fatigue, material can occur plastic deformation, uses a plastic correcting factor to carry out the plastic deformation of reaction material, i.e.
In formula: ρ is Hookean region size；σ0For material static(al) hot strength.
Consider the stress intensity amplitude of plastic correctingA' is the crack length considering plastic correcting, i.e. a'=a+ ρ.
(6) rust hole increases and crack Propagation competition mechanism
The impact of corrosion determined by step (5) is incorporated in step (4), obtains considering the fatigue crack growth rate model of corrosion impact, by the function that this model conversation is time t
Da/dt=C (Δ Kp(t)-ΔKth)mf(14)
In formula: f is repeatedly the frequency of vehicular load.
Along with being continuously increased of load, as it is shown on figure 3, there is a time point TtrSo that rust hole rate of rise is equal with crack growth rate, i.e.
(7) fatigue crack growth is to critical length
This stage progressively transfers reinforcing bar fatigue crack list growth mechanisms analysis to, can be by crackle model of growth realizes to critical crack length integration the life appraisal in this stage from equivalence initial crack size
In formula: acCrack critical length corresponding during for losing efficacy, fracture toughness and imposed load by material obtain.Fatigue load number N can be scaled time T by vehicular load frequency f according to bridge actual measurementcp。
Therefore, the aged reinforced concrete-bridge fatigue life-span is steel bar corrosion initial time Ti, reinforcing bar rust hole increase control time TtrTime T is controlled with reinforcing bar crack PropagationcpThese three stage sum.Calculation flow chart of the present invention is as shown in Figure 4.

Claims (5)

1. an aged reinforced concrete-bridge fatigue lifetime estimation method, it is characterised in that comprise the following steps:
Step one: based on Fick the second diffusion law, calculates concrete reinforcing steel surface chlorine ion concentration and reaches the time of marginal value, i.e. obtain corrosion initial time；
Step 2: use corrosion electric current density to represent steel bar corrosion speed, calculates the crack time and ftractures to the critical width time, obtaining considering the steel bar corrosion rate calculations model that rust distending splits impact；Fatigue of materials crack growth rate relevant parameter is determined by carrying out the fatigue crack propagation test of bar material, carry out corrosion reinforcing bar fatigue test or finite element analysis obtain under different erosion levels fatiguestrength reduction factor and be dissolved in stress intensity factor model, obtain reinforcing bar fatigue crack growth rate under the influence of corrosion, relatively rust hole rate of rise and fatigue crack growth rate size, obtain crack growth rate cheat with rust rate of rise equal time elapsed time；
Step 3: analyzed by reinforcing bar fatigue crack growth, to fatigue crack growth model from equivalence initial crack size to critical crack length integration, obtain the load periodicity occurring fatigue fracture to be experienced, in conjunction with measured load frequency, and then obtain the reinforcing bar crack Propagation control time.
Method the most according to claim 1, it is characterised in that described step one includes:
Based on Fick the second diffusion law, rebar surface chlorine ion concentration is reached the time of criticality chlorine ion concentration as corrosion initial time, corrode initial time TiIt is expressed as
In formula: TiFor reinforcement corrosion initial time；DcFor diffusion coefficient；C0For concrete surface chlorine ion concentration；Erf is error function；C is protective layer thickness；CcrFor criticality chlorine ion concentration.
Method the most according to claim 2, it is characterised in that described step 2 includes,
After t, the local erosion depth spot on concrete reinforcing steel surface is
P (t)=0.0116R ∫ icorr(t)dt(2)
In formula: p (t) is the rust hole degree of depth；R is corrosion nonuniformity coefficient；icorrT () is electric current density；T is the time；Corrosion starts t after current density
icorr(t)=32.1 (1-w/c)-1.64·(t-Ti)-0.29/C(3)
In formula: w/c is the ratio of mud；
It is simultaneously introduced accelerator coefficient kacConsider the crack impact on corrosion rate,
In formula: Tsp,limFor swollen crack and damage time of becoming rusty, Tsp,lim=Ti+Tcr+Tcc；TcrStart to cracking time for corrosion；TccFor cracking to boundary spaced time, wherein,
In formula: d0For gap thickness around reinforcing bar；D is bar diameter；υ is Poisson's ratio；ψ=(D+2d0)2/2C(C+D+2d0)；ftFor concrete tensile strength；EefFor concrete effective modulus of elasticity, Eef=Ec/(1+φcr)；EcFor modulus of elasticity of concrete；φcrFor creep coefficient；fcFor concrete strength；
In formula: WlimFor boundary width；
Rebar surface rust hole rate of rise is
Equivalence initial crack is expressed as
In formula: aiFor equivalence initial crack size；ΔKthFor critical stress intensity factors, in Fatigue Crack Growth Rate figure 10-10The value that m/ week is corresponding；ΔσfFor fatigue limit；Y is the Geometric corrections factor；Wherein Geometric corrections factor Y is expressed as
Y=G (0.752+1.286 β+0.37 ω3)(9)
In formula:ω=1-sin β；A is crack length；
Carrying out fatigue crack growth rate test, reinforcing bar Fatigue Crack Growth Rate is expressed as
Da/dN=C (Δ K-Δ Kth)m(10)
In formula: C, m are and material relevant parameter that the crack growth rate drawn by material crack way of extensive experimentation-stress intensive factor range curve matching obtains；N is fatigue life cycle；Δ K is stress intensive factor range,Δ σ is stress amplitude, Δ σ=σmax-σmin, reinforcement stresses size is calculated by finite element modelling or " Code for design of concrete structures GB50010-2010 " and obtains；Calculate the stress intensity factor under infection, on the basis of fatigue crack growth rate is tested, the impact that rust hole causes stress to concentrate is quantified, use following formula to calculate rust hole Root Stress intensity factor Kp(t), wherein, KtFor fatiguestrength reduction factor；
Fatiguestrength reduction factor uses Finite Element Method by reality rust hole size Modeling Calculation or to simplify calculating as the following formula
A plastic correcting factor is used to reflect the plastic deformation of material, i.e.
In formula: ρ is Hookean region size；σ0For material static(al) hot strength；
Consider the stress intensity amplitude of plastic correctingA' is the crack length considering plastic correcting, i.e. a'=a+ ρ；
Rust hole Root Stress intensity factor is introduced in fatigue crack growth rate is tested, obtains considering the fatigue crack growth rate model of corrosion impact, by the function that this model conversation is time t
Da/dt=C (Δ Kp(t)-ΔKth)mf(14)
In formula: f is repeatedly the frequency of vehicular load；
Along with being continuously increased of load, there is a time point TtrSo that rust hole rate of rise is equal with crack growth rate, i.e.
Method the most according to claim 3, it is characterised in that described step 3 includes,
By crackle model of growth is realized last life appraisal from equivalence initial crack size to critical crack length integration
In formula: acCrack critical length corresponding during for losing efficacy, fracture toughness and imposed load by material obtain, and according to vehicular load frequency f of bridge actual measurement, fatigue load number N are scaled time Tcp。
Method the most according to claim 1, it is characterised in that life appraisal includes three phases: steel bar corrosion initial time Ti, reinforcing bar rust hole increase control time TtrTime T is controlled with reinforcing bar crack Propagationcp。
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