CN104730222B - Nondestructive testing method for rusting degree of steel bar of reinforced concrete member after rusting cracking - Google Patents

Abstract

The invention discloses a nondestructive testing method for the rusting degree of a steel bar of a reinforced concrete member after rusting cracking. The method comprises the following steps: on the basis of mechanics of materials and theoretical mechanics, obtaining a formula (4-49), and measuring the crack width of the reinforced concrete member; if a stirrup is located at a corner part of the reinforced concrete member, calculating the mass of a rusting product according to the formula (4-51) or (4-53) or (4-49); if the stirrup is located in the middle of the reinforced concrete member, calculating according to the formula (4-52) or (4-54) or (4-49); calculating the masses of rusting products at different age periods and different crack widths; and calculating the rusting degree of the steel bar according to the masses of the rusting products, and judging the safety performance of the reinforced concrete member. The formula for nondestructive testing of the rusting degree of the steel bar is deduced on the basis of the mechanics of the materials and the theoretical mechanics. A half-experience and half-theory model disclosed by the invention is based on the theory, and is relatively wide in application range.

Description

Steel bar corrosion degree lossless detection method after a kind of reinforced concrete member corrosion cracking

Technical field

The present invention relates to steel bar corrosion degree lossless detection method after a kind of reinforced concrete member corrosion cracking.

Background technology

In the xoncrete structure of coastal area, the reinforcing bar in concrete often occurs different degrees of because of the erosion of chlorion Corrosion, produce split along muscle rust distending, the phenomenon such as sag of protecting coating, reinforcing bar are exposed.The loss of corrosion member reinforcing steel bar section, steel bars Hydraulic performance decline, reinforcing bar and concrete cooperative work performance reduce, and will directly affect usability and the security of structure.

Existing evaluation criteria thinks concrete cover once endurance life of ftractureing just terminates.However, substantial amounts of research Show, concrete cover rust distending splits initial stage, the corrosion ratio very little of reinforcing bar, and the bond performance between reinforcing bar and concrete there is no bright Aobvious degeneration, damage accumulation at this moment is also not enough to the bearing capacity of structure is constituted a threat to.In the durability evaluating of Practical Project, Fracture width is relatively easy to measurement and obtains, and is basic parameter during structure design simultaneously again.Thus, to concrete cover Fracture width extension after rust distending splits and ftractures is studied, in the case of not destroying structure safety, by visual examination Measurement, according to the relation between corrosive crack width and correlative factor, reasonably accurate carries out structure endurance life assessment, determines Maintenance and reinforcement measure and the Structure redesign based on durability, undoubtedly have realistic meaning.

Steel bar corrosion causes the process of concrete cover spalling considerably complicated, swollen damage process of both at home and abroad concrete being become rusty Before research is concentrated mainly on spalling, many scholars are based on substantial amounts of experimental study and theory analysis, when directly or indirectly providing spalling The computing formula of steel area corrosion ratio, form is different, respectively has pluses and minuses；Also scholar is had to pass through nonlinear finite element method swollen to becoming rusty Evolution and its influence factor be simulated analysis, but seldom provide corrosive crack width and reinforcing steel corrosion rate relational expression；Have Scholar is tested directly or indirectly to the steel area corrosion ratio computing formula having gone out based on corrosive crack width by Accelerated corrosion.

During the concrete cover swollen firm cracking of rust, the corrosion ratio very little of reinforcing bar, the bond performance between reinforcing bar and concrete is still No significant degradation, damage accumulation at this moment is also not enough to the bearing capacity of structure is constituted a threat to.As long as stoping the further of crack Extension, works, can be with normal work after small crack.The little altar of the Chinese architecture research institute residence of a high official proposes from spalling Width, protective layer thickness, bar diameter, Strength Forecast of Concrete steel area corrode the empirical equation of rate.This formula will not split Seam width is counted as an independent parameter, is suitable for engineering estimation.Total institute of designing institute of Ministry of Metallurgical Industry favour cloud tinkling of pieces of jade passes through real Test it is considered to concrete strength, protective layer thickness, bar diameter, reinforcement location, bar types and stirrup etc. under different spalling width The impact of parameter, 158 long-term expose on the basis of test specimens break type sampling actual measurement, relatively early propose strength grade c24～ Between c40, the relational expression of concrete component spalling width between 15～40mm for the protective layer thickness and steel area loss late. This formula is to compare the component under wet environment for northern China indoor and outdoor and propose, and form is simple, and assumes reinforcing bar rust Erosion rate is linearly proportional with corrosive crack width, has certain limitation.Andrade passes through impressed current accelerating corrosion The swollen test of rust it is believed that in the case that steel bar corrosion depth is less than certain value, reinforcing bar depth of corroding is linear with spalling width Proportionate relationship, and unrelated with parameters such as protective layer thickness, concrete strengths.Tongji University Wang Shen passes through having of rebar corrosion process The first sunykatuib analysis of limit, it calculates research and shows, spalling width relevant with reinforcing bar depth and linear it is proposed that from spalling width The formula of degree prediction steel area loss late.This formula form is simple, is easy to engineer applied, but the influence factor considering is less, As not yet considered the impact of the factors such as protective layer thickness, reinforcement location and stirrup.The computing formula that this formula is proposed with andrade Form is close, and the influence factor simply considering is less, and formula form also needs to improve further.Highway house of Department of Transportation Mao Yanji In more than 300 test specimens, respectively to reinforcing steel corrosion rate and surface crack under different concrete strengths, bar diameter, protective layer thickness The relation of width has carried out experimental study, establishes corresponding computing formula by the method returning." xoncrete structure is resistance to for China Property evaluation criteria long " also propose a steel bar corrosion depth calculation formula based on corrosive crack width.In view of empirical equation Theoretical foundation is not enough, on the basis of the steel bar corrosion amount forecast model before rust distending splits such as ox reed great waves, former based on corrosion electrochemistry Steel bar corrosion after reason is split to rust distending has carried out analyzing and giving computing formula, and this formula result of calculation discreteness is larger, And in Practical Project detection, model parameter is also difficult to determine.Later by becoming rusty to reinforcing bar before and after corrosive crack in Practical Project The analysis of erosion speed is it is proposed that a kind of approximate calculation method.In addition to above-mentioned computing formula, ox reed great waves et al. also apply nerve Network method predicts the relational model of reinforcing steel corrosion rate and fracture width, but this model to be applied to Practical Project relatively difficult. Summarize existing achievement in research, the theoretical calculation model of reinforcing steel corrosion rate research after concrete surface cracking is listed in the following table.

After table 2-1 concrete surface cracking, reinforcing steel corrosion rate theoretical model compares

Although there being numerous concrete surface cracks to occur with corrosion ratio relational model from the point of view of current present Research, Due to the difference of Consideration and starting point, result of calculation distribution is discrete very big.No matter this is because concrete itself is Still it is all the structure of highly each diversity from the point of view of microcosmic from macroscopic view, and the corrosion of reinforcement in concrete is not also always uniform 's；A lot of corrosion product meeting filling pores or part corrosion product can be along steel-concrete interfacial migrations.The number of corrosion product Amount depends greatly on the parameters such as thickness of concrete cover, corrosion product property and concrete properties.Existing warp at present Test the analysis of Influential Factors that model lays particular emphasis on steel bar corrosion, form is simply easy to apply, but lacks enough theoretical foundations, and by Emphasis in each researcher consideration is different and form is different.Up to the present, still do not have comprehensive and reasonable consider had an impact because The forecast model of the steel bar corrosion of element.Research to steel bar corrosion is more to start with from the aspect of material at present, seldom considers Influencing each other between different reinforcing bars (vertical muscle, stirrup) in practical structures, and this impact exactly can change the electricity of steel bar corrosion Chemical process.On the other hand, because rebar corrosion will lead to concrete cover to produce longitudinal crack along vertical muscle direction, when serious Cover concrete can be led to peel off.With the extension in spalling crack, the bonding degree of concrete and rebar can decline；Work as protective layer When coming off, reinforcing bar can aggravate due to losing protective barrier, the corrosion rate of reinforcing bar.But this process development is actually to xoncrete structure Produce the impact of which kind of degree, also not fully aware of at present.Further investigation to this process, it will help heightened awareness concrete Become rusty swollen mechanism, for controlling the swollen development offer measure of concrete rust, and be that steel bar corrosion is estimated according to corrosive crack width detection Rate provides basis.

In the higher environment of chloride ion content, chlorion, by diffusing into inside concrete, destroys rebar surface Passivating film, cause reinforcing bar to get rusty and expand, further result in that surface concrete cracks and flakes off, xoncrete structure uses function Continuous degeneration with mechanical property.Concrete cover rust distending split be generally divided into iron rust free wxpansion, concrete cover holds Tension stress and concrete cover rust distending split three phases.Specifically describe as shown in Figure 1.

Fig. 1 can be specifically described as:

First stage is just to have built up concrete from structure to corrode due to harmful ions such as carbonization or chlorions, causes reinforcing bar Damage of Passive Film, that is, take off the blunt stage；

Second stage is from steel-bar corrosion to the existing crack of concrete cover invar muscle rust expansion, i.e. crack initiation stage；

Phase III from crack, due to the development in crack lead to structure applicable performance reduce, carry Ability reduces or region property is destroyed.

Three key points that three phases are formed are most important to research structure durability.First key point mark steel Muscle take off blunt started become rusty；Second key point mark steel bar corrosion development, until crack；3rd key point Mean that the degree of safety leading to structure due to the expansion in crack can not meet requirement.

The foundation that current measurement removing blunt of reinforcing steel bar plays rust mainly has two: carbonation depth reaches rebar surface；Amount of chloride ions accounts for In concrete, the percentage of cement amount reaches a certain restriction.On this basis, by the speed of concrete carbonization or the expansion of chlorion Using fick second law, scattered speed, is assured that reinforced concrete structure plays the time t of rust_cor.

For second stage, that is, rebar corrosion leads to the cracking role of concrete cover, the standard of protective layer cracking time Really calculate particularly significant, because it is an important critical point of evaluation structure service life.The swollen cracking model that become rusty is main Based on the concrete homogeneous same sex it is assumed that being derived by by theory of elastic mechanics.With respect to equal and corrosion, due to studying difficulty relatively Greatly, meet the actual uneven corrosion research of engineering and compare shortage.Substantial amounts of research, Zhang Wei are carried out for this stage both at home and abroad Flat, Niu Ditao, Jin Weiliang, Zhang Yu etc. have carried out systematic research.

For the phase III, after crack, rust swelling pressure power will make fracture width be stepped up, due to theory Analysis difficulty is larger, thus correlation theory scale-model investigation is still at an early stage.2006, li chunqing and zheng Jianjun etc. supposes that crack is uniformly distributed along around reinforcing bar, and thinks that non-cracked concrete is homogeneous elasticity, considers to open simultaneously Split the softening performance of concrete, establish corrosive crack width theoretical model first, be that follow-up study provides preferable research Background and basic achievement.2012, the side based on dimensional effect and fracture mechanics such as zhang xiaogang and wang jiao Method, it is contemplated that the size of the initial porosity defects in concrete reinforcing steel surface, using cantilever beam moment of flexure-load computational methods, is set up The concrete surface distending that becomes rusty splits the theoretical model of width.Additionally, the scholar such as the army of defending, Jin Weiliang, Zhou Xiwu has been also carried out correlation Theoretical research.

At present, researcher causes the common understanding of concrete surface dehiscence process, its schematic diagram for steel bar corrosion As shown in Figure 2.

In Fig. 2, d is bar diameter；C is thickness of concrete cover；R is the distance to protective layer center for the reinforcing steel bar center, r ≈(d+c)/2；d₀Thickness for concrete pore at reinforcing bar and concrete surface；A is the length of initial imperfection in concrete； The bulbs of pressure that p causes for rebar corrosion；p₀For swelling stress threshold value during crack；δ a expands for effective fracture Length degree；w₀The crack developing original width leading to for steel bar corrosion；U, v are respectively the displacement at point o along s axle and y-axis.

As shown in Figure 2, concrete surface crack development is strong with bar diameter, thickness of concrete cover, concrete tension The factors such as degree are directly related, and the analysis of design parameter can be analyzed on the basis of test and theory further.

In reinforced concrete member, steel bar corrosion can produce material impact to the unfailing performance of component, and detection reinforcing bar mixed in the past In solidifying soil component, the method for steel bar corrosion amount mainly takes the method for testing of corrosion electric current density, before being directed to corrosion cracking Stage, and for corrosion cracking after steel bar corrosion degree test, there is presently no maturation lossless detection method.

Content of the invention

It is an object of the invention to solving at least the above and/or defect, and provide at least will be described later excellent Point.

It is a still further object of the present invention to provide the lossless inspection of steel bar corrosion degree after a kind of reinforced concrete member corrosion cracking Survey method, applies the present invention, steel bar corrosion degree can be entered with Mobile state and observe it is ensured that the unfailing performance of component, judge in crack width Degree reaches the component security performance before threshold limit value.

It is a still further object of the present invention to provide derived based on the mechanics of materials and rational mechanics and test data etc. The formula of steel bar corrosion degree Non-Destructive Testing, the model of half that the present invention derives has theory as foundation, applicable model Enclose more extensive, overcome and carry out the derivation of equation only with test data, there is no theory as foundation, the formula derived is suitable for model It is with the problem of limit.

The technical scheme that the present invention provides is:

Steel bar corrosion degree lossless detection method after a kind of reinforced concrete member corrosion cracking, comprises the steps:

Step one, be based on the mechanics of materials and rational mechanics, obtain equation below (4-49),

$w_{\mathrm{rust}}\left(t\right)=\frac{(w_c+\frac{2\mathrm{\πb}{f}_t}{e_{\mathrm{ef}}})\·(d+2d_0)\·[(1-v_c){(a/b)}^{\sqrt{\mathrm{\α}}}+(1+v_c){(b/a)}^{\sqrt{\mathrm{\α}}}]}{4\·(\frac{1}{{\mathrm{\ρ}}_{\mathrm{rust}}}-\frac{{\mathrm{\α}}_{\mathrm{rust}}}{{\mathrm{\ρ}}_{\mathrm{st}}})}---(4-49)$

Wherein, e_efFor concrete effective modulus of elasticity, d is bar diameter, d₀For mixing between reinforcing bar and concrete binding interface Coagulate the thickness of rustic hole endless belt, v_cFor concrete Poisson's ratio, c is thickness of concrete cover, a=(d+2d₀)/2, b=c+ (d +2d₀)/2, α is concrete Stiffness degradation coefficient, ρ_rustFor corrosion product density, ρ_stFor reinforcing bar density and α_rustIt is and corrosion The related coefficient of product types；According to document liu, y., and weyers, r.e.modeling the time-to- corrosion cracking in chloride contaminated reinforced concrete structures [j] .aci mater.journal, 1998,95 (6): 675-681 ", by α_rustBe construed to related to corrosion product type be Number, refers to that the corrosion product of reinforcing bar has many kinds, such as iron oxide, iron hydroxide etc..

Step 2, the fracture width w of measurement reinforced concrete member_cValue, according to the calculated corrosion of formula (4-49) Product quality w_rustT () value, calculates the steel bar corrosion degree of this reinforced concrete member, afterwards to judge this reinforced concrete member Security performance.

Preferably, in steel bar corrosion degree lossless detection method after described reinforced concrete member corrosion cracking, described In step 2, if stirrup is located at the corner of this reinforced concrete member, being calculated according to equation below (4-51) has steel during stirrup Quality w of muscle corrosion product_{There is stirrup},

Wherein, w_{No stirrup}It is corrosion product quality w being obtained according to formula (4-49)_rustT () value, e is the springform of stirrup Amount, l_svFor stirrup length on member section, g is concrete shearing modulus,A represents mixed The area that solidifying soil is affected by stirrup, a=c s, wherein, c represents thickness of concrete cover, and s represents stirrup spacing, i=(1/ 12)s·c³, k=1.2, d are stirrup diameter, a_sv1Represent the sectional area of single hoop muscle, e_svElastic modelling quantity for stirrup.

Even more preferably, in steel bar corrosion degree lossless detection method after described reinforced concrete member corrosion cracking, order $\mathrm{\λ}=\frac{d}{c},\mathrm{\β}=\frac{e_{\mathrm{sv}}}{e_c},{\mathrm{\ρ}}_{\mathrm{sv}}^{\′}=\frac{a_{\mathrm{sv}}}{b\·s},$ Then have:

Preferably, in steel bar corrosion degree lossless detection method after described reinforced concrete member corrosion cracking, described In step 2, if stirrup is located at the middle part of this reinforced concrete member, being calculated according to equation below (4-52) has steel during stirrup Quality w of muscle corrosion product_{There is stirrup},

Wherein, w_{No stirrup}It is corrosion product quality w being obtained according to formula (4-49)_rustT () value, e is the springform of stirrup Amount, l_svFor stirrup length on member section, g is concrete shearing modulus,A represents mixed The area that solidifying soil is affected by stirrup, a=c s, wherein, c represents thickness of concrete cover, and s represents stirrup spacing, i=(1/ 12)s·c³, k=1.2, d are stirrup diameter, a_sv1Represent the sectional area of single hoop muscle, e_svElastic modelling quantity for stirrup.

Even more preferably, in steel bar corrosion degree lossless detection method after described reinforced concrete member corrosion cracking, its It is characterised by, order $\mathrm{\λ}=\frac{d}{c},\mathrm{\β}=\frac{e_{\mathrm{sv}}}{e_c},{\mathrm{\ρ}}_{\mathrm{sv}}^{\′}=\frac{a_{\mathrm{sv}}}{b\·s},$ Then have:

Preferably, in steel bar corrosion degree lossless detection method after described reinforced concrete member corrosion cracking, described In step one, the detailed process obtaining formula (4-49) includes:

(1.1) it is based on the mechanics of materials and rational mechanics, swollen for the rust of concrete cover crack and damage influence area is simplified For the thick cyclinder of Space Axisymmetric, then have,

The internal-and external diameter of concrete cover thick cyclinder is respectively as follows: a=(d+2d₀)/2, b=c+ (d+2d₀)/2；

Corrosion product thickness d_sT () is:

$d_s\left(t\right)=\frac{w_{\mathrm{rust}}\left(t\right)}{\mathrm{\π}(d+2d_0)}(\frac{1}{{\mathrm{\ρ}}_{\mathrm{rust}}}-\frac{{\mathrm{\α}}_{\mathrm{rust}}}{{\mathrm{\ρ}}_{\mathrm{st}}})---(4-1)$

(1.2) determine the basic parameter value of reinforced concrete member, including bar diameter d, thickness of concrete cover c, Concrete tensile strength f_t, concrete Poisson's ratio v_c, simultaneous formula (4-39), (4-40) and (4-42), c can be tried to achieve₅, c₆And α；)

$c_5=\frac{(1-v_c)a^{\sqrt{\mathrm{\α}}}}{(1-v_c)a^{2\sqrt{\mathrm{\α}}}+(1+v_c)b^{2\sqrt{\mathrm{\α}}}}{d}_s\left(t\right)---(4-39)$

$c_6=\frac{(1+v_c)a^{\sqrt{\mathrm{\α}}}{b}^{2\sqrt{\mathrm{\α}}}}{(1-v_c)a^{2\sqrt{\mathrm{\α}}}+(1+v_c)b^{2\sqrt{\mathrm{\α}}}}{d}_s\left(t\right)---(4-40)$

$\mathrm{\α}=\frac{f_t\exp \{-\mathrm{\γ}[(b^{\sqrt{\mathrm{\α}}}-a^{\sqrt{\mathrm{\α}}})[c_5+c_6/{\left(\mathrm{ab}\right)}^{\sqrt{\mathrm{\α}}}]/\sqrt{\mathrm{\α}}(b-a)-\frac{1}{b-a}\mathrm{\ω}\left]\right\}}{\frac{e_{\mathrm{ef}}(b^{\sqrt{\mathrm{\α}}}-a^{\sqrt{\mathrm{\α}}})[c_5+c_6/{\left(\mathrm{ab}\right)}^{\sqrt{\mathrm{\α}}}]}{\sqrt{\mathrm{\α}}(b-a)}}---(4-42)$

Wherein γ is concrete material constant；

(1.3) utilize the c obtaining in step (1.2)₅, c₆And α, according to formula (4-46), obtain concrete surface cracking Fracture width w_cWith steel bar corrosion product thickness d_sThe calculation expression of (t)；

$\begin{array}{c}{w}_c=2\mathrm{\πb}[c_5{b}^{(\sqrt{\mathrm{\α}}-1)}+c_6{b}^{(-\sqrt{\mathrm{\α}}-1)}-\frac{f_t}{e_{\mathrm{ef}}}]\\ =\frac{4\mathrm{\π}{d}_s\left(t\right)}{(1-v_c){(a/b)}^{\sqrt{\mathrm{\α}}}+(1+v_c){(b/a)}^{\sqrt{\mathrm{\α}}}}-\frac{2\mathrm{\πb}{f}_t}{e_{\mathrm{ef}}}\end{array}---(4-46)$

(1.4) simultaneous formula (4-1) and (4-46), obtains steel bar corrosion product quality w_rustT () is opened with concrete surface Split width w_cCalculation expression formula (4-49).

Even more preferably, in steel bar corrosion degree lossless detection method after described reinforced concrete member corrosion cracking, institute State the multigroup numerical value obtaining concrete Stiffness degradation factor alpha in step (1.2) according to formula (4-42), then recycle spss Software carries out returning calculating, obtains equation below (4-47),

α=0.01137638 × (t/365)^{(-2.198836253)}+0.1235655576(r²=0.974) (4-47)

Calculate the armored concrete structure under different larval instar and different fracture width using formula (4-47) and formula (4-49) The reinforcing steel corrosion rate of part.

Even more preferably, in steel bar corrosion degree lossless detection method after described reinforced concrete member corrosion cracking, institute State in step (1.2),e_cRepresent 28 days elastic modelling quantity of concrete,For concrete creep coefficient

The present invention at least includes following beneficial effect:

The application present invention, can only pass through to measure fracture width, you can to steel in the case of lossless reinforced concrete member Muscle degree of rusting enters Mobile state to be observed it is ensured that the unfailing performance of component, judges the component before fracture width reaches threshold limit value Security performance.

The method of the present invention is simple and easy to operate, and reinforcing bar modification rate under different larval instar, different cracking width can be calculated, For judging reinforced concrete member state in which, its degree of wear, thus judge its security.

Instant invention overcomes traditionally carrying out the derivation of equation only with test data, there is no theory as foundation, deriving Formula restricted application problem, but on the basis of theory, based on the mechanics of materials and rational mechanics and test data Etc. the formula of the steel bar corrosion degree Non-Destructive Testing derived, the model of half that the present invention derives has theoretical conduct Foundation, the scope of application is more extensive.Part is embodied by the further advantage of the present invention, target and feature by description below, part Also will be understood by the person skilled in the art by research and practice to the present invention.

Brief description

Fig. 1 is that corrosion degree deteriorates relation model figure with component performance；

Fig. 2 causes concrete surface crack evolution schematic diagram for steel bar corrosion, and wherein, (a) is initial in concrete Hole and defect schematic diagram, (b) is crack progressing schematic diagram, and (c) is crack schematic diagram, and (d) is initially to open Split width calculation model schematic；

Fig. 3 is that the steel bar corrosion in the one of embodiment of the present invention causes crack process schematic, Wherein, (a) is initial hole and defect schematic diagram in concrete, and (b) is crack progressing schematic diagram, and (c) is concrete cover Cracking schematic diagram；

Fig. 4 tests for fracture width under the Different Water-Cement Ratio in the one of embodiment of the present invention and reinforcing steel corrosion rate relation Value and model calculation value comparison diagram (d=25mm)；

Fig. 5 is fracture width and reinforcing steel corrosion rate relation test value and different models in the one of embodiment of the present invention Calculated value comparison diagram.

Specific embodiment

The present invention is described in further detail below in conjunction with the accompanying drawings, to make those skilled in the art with reference to specification literary composition Word can be implemented according to this.

It should be appreciated that used in the present invention such as " have ", "comprising" and " inclusion " term do not allot one or The presence of multiple other elements or a combination thereof or interpolation.

As shown in Fig. 3～Fig. 5, the present invention provides the lossless inspection of steel bar corrosion degree after a kind of reinforced concrete member corrosion cracking Survey method, comprises the steps:

Step one, be based on the mechanics of materials and rational mechanics, obtain equation below (4-49),

$w_{\mathrm{rust}}\left(t\right)=\frac{(w_c+\frac{2\mathrm{\πb}{f}_t}{e_{\mathrm{ef}}})\·(d+2d_0)\·[(1-v_c){(a/b)}^{\sqrt{\mathrm{\α}}}+(1+v_c){(b/a)}^{\sqrt{\mathrm{\α}}}]}{4\·(\frac{1}{{\mathrm{\ρ}}_{\mathrm{rust}}}-\frac{{\mathrm{\α}}_{\mathrm{rust}}}{{\mathrm{\ρ}}_{\mathrm{st}}})}---(4-49)$

Wherein, e_efFor concrete effective modulus of elasticity, d is bar diameter, d₀For mixing between reinforcing bar and concrete binding interface Coagulate the thickness of rustic hole endless belt, v_cFor concrete Poisson's ratio, c is thickness of concrete cover, a=(d+2d₀)/2, b=c+ (d +2d₀)/2, α is concrete Stiffness degradation coefficient, ρ_rustFor corrosion product density, ρ_stFor reinforcing bar density and α_rustIt is and corrosion The related coefficient of product types；According to document liu, y., and weyers, r.e.modeling the time-to- corrosion cracking in chloride contaminated reinforced concrete structures [j] .aci mater.journal, 1998,95 (6): 675-681 ", by α_rustBe construed to related to corrosion product type be Number, refers to that the corrosion product of reinforcing bar has many kinds, such as iron oxide, iron hydroxide etc..

Step 2, the fracture width w of measurement reinforced concrete member_cValue, is calculated corrosion using formula (4-49) and produces Amount of substance w_rustT () value, calculates the steel bar corrosion degree of this reinforced concrete member, afterwards to judge this reinforced concrete member Security performance.

For the test of steel bar corrosion degree after corrosion cracking, there is presently no the lossless detection method of maturation.Present invention profit The corrosion degree of reinforcing bar can be embodied with the width in crack, in conjunction with concrete material characteristic, rebar sizes and protection thickness The parameters such as degree, can be with the corrosion amount of internal reinforcing bar after Non-Destructive Testing concrete component corrosion cracking.Application the method, can be to reinforcing bar Degree of rusting enters Mobile state observation it is ensured that the unfailing performance of component.According to existing such as " durability design rule Model " etc. specification, the method according to the invention can determine whether out that fracture width reaches or the peace beyond the component after threshold limit value Full performance, also more meaningful.

Preferably, in described step 2, if stirrup is located at the corner of this reinforced concrete member, according to equation below (4-51) calculating has quality w of steel bar corrosion product during stirrup_{There is stirrup},

Wherein, w_{No stirrup}It is corrosion product quality w being obtained according to formula (4-49)_rustT () value, e is the springform of stirrup Amount, l_svFor stirrup length on member section, g is concrete shearing modulus,A represents mixed The area that solidifying soil is affected by stirrup, a=c s, wherein, c represents thickness of concrete cover, and s represents stirrup spacing, i=(1/ 12)s·c³, k=1.2, d are stirrup diameter, a_sv1Represent the sectional area of single hoop muscle, e_svElastic modelling quantity for stirrup.

Preferably, in above-mentioned scheme, orderThen have:

Preferably, in described step 2, if stirrup is located at the middle part of this reinforced concrete member, according to equation below (4-52) calculating has quality w of steel bar corrosion product during stirrup_{There is stirrup},

Wherein, w_{No stirrup}It is corrosion product quality w being obtained according to formula (4-49)_rustT () value, e is the springform of stirrup Amount, l_svFor stirrup length on member section, g is concrete shearing modulus,A represents mixed The area that solidifying soil is affected by stirrup, a=c s, wherein, c represents thickness of concrete cover, and s represents stirrup spacing, i=(1/ 12)s·c³, k=1.2, d are stirrup diameter, a_sv1Represent the sectional area of single hoop muscle, e_svElastic modelling quantity for stirrup.

Preferably, in above-mentioned scheme, orderThen have:

Preferably, in described step one, the detailed process obtaining formula (4-49) includes:

(1.1) it is based on the mechanics of materials and rational mechanics, swollen for the rust of concrete cover crack and damage influence area is simplified For the thick cyclinder of Space Axisymmetric, then have,

The internal-and external diameter of concrete cover thick cyclinder is respectively as follows: a=(d+2d₀)/2, b=c+ (d+2d₀)/2；

Corrosion product thickness d_sT () is:

$d_s\left(t\right)=\frac{w_{\mathrm{rust}}\left(t\right)}{\mathrm{\π}(d+2d_0)}(\frac{1}{{\mathrm{\ρ}}_{\mathrm{rust}}}-\frac{{\mathrm{\α}}_{\mathrm{rust}}}{{\mathrm{\ρ}}_{\mathrm{st}}})---(4-1)$

(1.2) determine the basic parameter value of reinforced concrete member, including bar diameter d, thickness of concrete cover c, Concrete tensile strength f_t, concrete Poisson's ratio v_c, simultaneous formula (4-39), (4-40) and (4-42), c can be tried to achieve₅, c₆And α；)

$c_5=\frac{(1-v_c)a^{\sqrt{\mathrm{\α}}}}{(1-v_c)a^{2\sqrt{\mathrm{\α}}}+(1+v_c)b^{2\sqrt{\mathrm{\α}}}}{d}_s\left(t\right)---(4-39)$

$c_6=\frac{(1+v_c)a^{\sqrt{\mathrm{\α}}}{b}^{2\sqrt{\mathrm{\α}}}}{(1-v_c)a^{2\sqrt{\mathrm{\α}}}+(1+v_c)b^{2\sqrt{\mathrm{\α}}}}{d}_s\left(t\right)---(4-40)$

$\mathrm{\α}=\frac{f_t\exp \{-\mathrm{\γ}[(b^{\sqrt{\mathrm{\α}}}-a^{\sqrt{\mathrm{\α}}})[c_5+c_6/{\left(\mathrm{ab}\right)}^{\sqrt{\mathrm{\α}}}]/\sqrt{\mathrm{\α}}(b-a)-\frac{1}{b-a}\mathrm{\ω}\left]\right\}}{\frac{e_{\mathrm{ef}}(b^{\sqrt{\mathrm{\α}}}-a^{\sqrt{\mathrm{\α}}})[c_5+c_6/{\left(\mathrm{ab}\right)}^{\sqrt{\mathrm{\α}}}]}{\sqrt{\mathrm{\α}}(b-a)}}---(4-42)$

Wherein γ is concrete material constant；f_tThe tensile strength of concrete；Exp is exponential function form, i.e. function exp (x)=e^x.

(1.3) utilize the c obtaining in step (1.2)₅, c₆And α, according to formula (4-46), obtain concrete surface cracking Fracture width w_cWith steel bar corrosion product thickness d_sThe calculation expression of (t)；

$\begin{array}{c}{w}_c=2\mathrm{\πb}[c_5{b}^{(\sqrt{\mathrm{\α}}-1)}+c_6{b}^{(-\sqrt{\mathrm{\α}}-1)}-\frac{f_t}{e_{\mathrm{ef}}}]\\ =\frac{4\mathrm{\π}{d}_s\left(t\right)}{(1-v_c){(a/b)}^{\sqrt{\mathrm{\α}}}+(1+v_c){(b/a)}^{\sqrt{\mathrm{\α}}}}-\frac{2\mathrm{\πb}{f}_t}{e_{\mathrm{ef}}}\end{array}---(4-46)$

(1.4) simultaneous formula (4-1) and (4-46), obtains steel bar corrosion product quality w_rustT () is opened with concrete surface Split width w_cCalculation expression formula (4-49).

Preferably, in above-mentioned scheme, in described step (1.2), according to test data and document li c q, Zheng j j, lawanwisut w and melchers r e.concrete delamination caused by steel Reinforcement corrosion [j] .journal of materials in civil engineering, 2007,19 (7): 591-600. and li chunqing, yang yang and melchers robert e.prediction of reinforcement corrosion in concrete and its effects on concrete cracking and Strength reduction [j] .aci materials journal, 2008,105 (1): 3-10. and document li c q and yang s t.prediction of concrete crack width under combined reinforcement Corrosion and applied load [j] .journal of engineering mechanics, 2011,137 (11): Data in 722-731, by the tensile strength of concrete, the effective elasticity model of concrete, bar diameter, reinforcing bar concrete Protective layer thickness parameter is updated to multigroup numerical value that formula (4-42) obtains concrete Stiffness degradation factor alpha as shown in table 1, so Recycle spss software to carry out returning calculating afterwards, obtain equation below (4-47),

α=0.01137638 × (t/365)^{(-2.198836253)}+0.1235655576(r²=0.974) (4-47)

Calculate the armored concrete structure under different larval instar and different fracture width using formula (4-47) and formula (4-49) The reinforcing steel corrosion rate of part.

Preferably, in described step (1.2),e_cRepresent 28 days elastic modelling quantity of concrete,For Concrete creep coefficient.

In one embodiment of the invention, as shown in figure 3, d is bar diameter；d₀For reinforcing bar and concrete binding interface Between concrete pore endless belt thickness, after concrete hardening, d₀Constant can be regarded as；C is thickness of concrete cover；Coagulation The internal-and external diameter of protective soil layer thick cyclinder is respectively a=(d+2d₀)/2, b=c+ (d+2d₀)/2；d_sT () is corrosion product thickness, Can be tried to achieve by formula (4-1):

$d_s\left(t\right)=\frac{w_{\mathrm{rust}}\left(t\right)}{\mathrm{\π}(d+2d_0)}(\frac{1}{{\mathrm{\ρ}}_{\mathrm{rust}}}-\frac{{\mathrm{\α}}_{\mathrm{rust}}}{{\mathrm{\ρ}}_{\mathrm{st}}})---(4-1)$

In above formula, α_rustIt is the coefficient related to corrosion product type；ρ_rustFor corrosion product density；ρ_stClose for reinforcing bar Degree；w_rustT () is corrosion product quality

Due to the continuous growth of corrosion product, stress is created to concrete.Under the effect of this expansive force, concrete is protected The crack form of sheath experienced three phases: 1) no ftractures；2) part ftractures；3) instant of complete cracking.For no ftractureing the stage, mix Solidifying soil thick cyclinder (protective layer) can regard isotropic elastic body as, therefore can calculate any point on cylinder with elastic theory Radial stress σ of (r)_r(r) and tangential stress σ_θ(r).According to radial stress σ_r(r), the expansion between corrosion product and concrete Stress p₁Can be expressed as:

$p_1=-{\mathrm{\σ}}_r\left(a\right)=\frac{e_{\mathrm{ef}}{d}_s\left(t\right)}{a(\frac{b^2+a^2}{b^2-a^2}+v_c)}---(4-3)$

Wherein, e_efFor concrete effective modulus of elasticity,For concrete creep coefficient, e_cRepresent 28 days elastic modelling quantity of concrete；v_cFor concrete Poisson's ratio.

According to tangential stress σ at r=a_θ(r), concrete cover initial cracking time t₁Can be by condition σ_θ(a)=f_tCertainly Fixed, wherein f_tFor concrete tensile strength.

According to timoshenko and goodier, under cylindrical radial displacement u (r) of non-cracked concrete should meet Formula:

$\frac{d^{2}u\left(r\right)}{d{r}^2}+\frac{1}{r}\·\frac{\mathrm{du}\left(r\right)}{\mathrm{dr}}-\frac{u\left(r\right)}{r^2}=0---(4-4)$

It will be evident that the solution of u (r) is in formula (4-4):

$u\left(r\right)=c_1\left(r_0\right)r+\frac{c_2\left(r_0\right)}{r}---(4-5)$

In above formula, coefficient c₁(r₀) and c₂(r₀) it is r₀Function, excursion is between a and b.Therefore, do not ftracture coagulation On protective soil layer, the radially and tangentially stress of any point (r) is respectively as follows:

${\mathrm{\σ}}_r\left(r\right)=\frac{e_{\mathrm{ef}}}{1-v_c^2}[(1+v_c)c_1\left(r_0\right)-\frac{(1-v_c)c_2\left(r_0\right)}{r^2}]---(4-6)$

${\mathrm{\σ}}_{\mathrm{\θ}}\left(r\right)=\frac{e_{\mathrm{ef}}}{1-v_c^2}[(1+v_c)c_1\left(r_0\right)+\frac{(1-v_c)c_2\left(r_0\right)}{r^2}]---(4-7)$

For internal cleavage concrete cylinder it is assumed that crack is uniformly distributed in disperse, and concrete is quasi-brittle material.Cause This, fracture mechanics can be used for the analysis cylindrical stress distribution situation of cracking.In cracking interval [a, r₀], remaining shear stiffness can It is expressed as α e_ef, wherein α (＜ 1) is shear stiffness reduction coefficient.According to bazant and planas, shear stiffness reduction coefficient Average tangential strain on α and fracture surfaceCorrelation, is represented by:

$\mathrm{\α}=\frac{f_t\exp [-\mathrm{\γ}(\stackrel{\&overbar;}{{\mathrm{\ϵ}}_{\mathrm{\θ}}}-\stackrel{\&overbar;}{{\mathrm{\ϵ}}_{\mathrm{\θ}}^c})]}{e_{\mathrm{ef}}\stackrel{\&overbar;}{{\mathrm{\ϵ}}_{\mathrm{\θ}}}}---(4-8)$

In formula (4-8),Represent averagely tangential cracking strain；γ is material constant.

Due to the impact of radial direction cracking, the concrete near crack is believed that anisotropic material.Namely radial direction Modulus of elasticity of concrete different from tangential direction, therefore, cracking part concrete is radially and tangential constitutive relation is:

${\mathrm{\σ}}_r\left(r\right)=\frac{e_{\mathrm{ef}}}{1-v_1{v}_2}[{\mathrm{\ϵ}}_r\left(r\right)+v_2{\mathrm{\ϵ}}_{\mathrm{\θ}}\left(r\right)]---(4-9)$

${\mathrm{\σ}}_{\mathrm{\θ}}\left(r\right)=\frac{\mathrm{\α}{e}_{\mathrm{ef}}}{1-v_1{v}_2}[{\mathrm{\ϵ}}_{\mathrm{\θ}}\left(r\right)+v_1{\mathrm{\ϵ}}_r\left(r\right)]---(4-10)$

In formula (4-9) and (4-10), v₁And v₂It is respectively radially and tangentially concrete Poisson's ratio.Required based on anisotropy v₂e_ef=v₁αe_ef ^[55]With approximateFormula (4-9) and (4-10) can be written as further:

${\mathrm{\σ}}_r\left(r\right)=\frac{e_{\mathrm{ef}}}{1-v_c^2}[{\mathrm{\ϵ}}_r\left(r\right)+v_c\sqrt{\mathrm{\α}}{\mathrm{\ϵ}}_{\mathrm{\θ}}\left(r\right)]---(4-11)$

${\mathrm{\σ}}_{\mathrm{\θ}}\left(r\right)=\frac{e_{\mathrm{ef}}}{1-v_c^2}[\mathrm{\α}{\mathrm{\ϵ}}_{\mathrm{\θ}}\left(r\right)+v_c\sqrt{\mathrm{\α}}{\mathrm{\ϵ}}_r\left(r\right)]---(4-12)$

When concrete cylinder (protective layer) no external force effect, radial direction stress equilibrium need to meet following formula condition:

$\frac{\&partiald;{\mathrm{\σ}}_r\left(r\right)}{\&partiald;r}+\frac{{\mathrm{\σ}}_r\left(r\right)-{\mathrm{\σ}}_{\mathrm{\θ}}\left(r\right)}{r}=0---(4-13)$

Strain-displacement coordination needs to meet:

${\mathrm{\ϵ}}_r=\frac{\mathrm{du}\left(r\right)}{\mathrm{dr}}---(4-14)$

${\mathrm{\ϵ}}_{\mathrm{\θ}}\left(r\right)=\frac{u\left(r\right)}{r}---(4-15)$

By formula (4-11), (4-12), (4-14) and (4-15) substitutes in formula (4-13), can obtain:

$\frac{d^{2}u\left(r\right)}{d{r}^2}+\frac{1}{r}\·\frac{\mathrm{du}\left(r\right)}{\mathrm{dr}}-\mathrm{\α}\frac{u\left(r\right)}{r^2}=0---(4-16)$

Formula (4-16) is cracked concrete cylinder Bit andits control equation.The solution of formula (4-16) is:

$u\left(r\right)=c_3\left(r_0\right)r^{\sqrt{\text{\α}}}+c_4\left(r_0\right)r^{-\sqrt{\mathrm{\α}}}---(4-17)$

In above formula, coefficient c₃(r₀) and c₄(r₀) it is still r₀Function, radially and tangentially stress is respectively as follows: accordingly

${\mathrm{\σ}}_r\left(r\right)=\frac{\sqrt{\mathrm{\α}}{e}_{\mathrm{ef}}}{1-v_c^2}[c_3\left(r_0\right)(1+v_c)r^{(\sqrt{\mathrm{\α}}-1)}-c_4\left(r_0\right)(1-v_c)r^{(-\sqrt{\mathrm{\α}}-1)}]---(4-18)$

${\mathrm{\σ}}_{\mathrm{\θ}}\left(r\right)=\frac{\mathrm{\α}{e}_{\mathrm{ef}}}{1-v_c^2}[c_3\left(r_0\right)(1+v_c)r^{(\sqrt{\mathrm{\α}}-1)}+c_4\left(r_0\right)(1-v_c)r^{(-\sqrt{\mathrm{\α}}-1)}]---(4-19)$

The cylindrical boundary condition of concrete cover is:

$(1+v_c)c_1\left(r_0\right)-\frac{(1-v_c)c_2\left(r_0\right)}{b^2}=0---(4-20)$

$c_3\left(r_0\right)a^{\sqrt{\mathrm{\α}}}+c_4\left(r_0\right)a^{-\sqrt{\mathrm{\α}}}=d_s\left(t\right)---(4-21)$

Meet in r₀Place's displacement and radial strain continuously require, that is,

$c_1\left(r_0\right)r_0+\frac{c_2\left(r_0\right)}{r_0}=c_3\left(r_0\right){r_0}^{\sqrt{\mathrm{\α}}}+c_4\left(r_0\right){r_0}^{-\sqrt{\mathrm{\α}}}---(4-22)$

$(1+v_c)c_1\left(r_0\right)-\frac{(1-v_c)c_2\left(r_0\right)}{r_0^2}=\sqrt{\mathrm{\α}}[(1+v_c){r_0}^{(\sqrt{\mathrm{\α}}-1)}{c}_3\left(r_0\right)-(1-v_c){r_0}^{(-\sqrt{\mathrm{\α}}-1)}{c}_4\left(r_0\right)]---(4-23)$

Therefore, by solution formula (4-20)～(4-23), can get c₁(r₀), c₂(r₀), c₃(r₀) and c₄(r₀):

$c_1\left(r_0\right)=-\frac{2\sqrt{\mathrm{\α}}(1-v_c)r_0{d}_s\left(t\right)}{\mathrm{\δ}}---(4-24)$

$c_2\left(r_0\right)=-\frac{2\sqrt{\mathrm{\α}}(1+v_c)r_0{b}^2{d}_s\left(t\right)}{\mathrm{\δ}}---(4-25)$

$c_3\left(r_0\right)=-\frac{\{(1-v_c)(\sqrt{\mathrm{\α}}-1)b^2+[1+v_c+\sqrt{\mathrm{\α}}(1-v_c)\left]r_0^2\right\}\mathrm{\ψ}}{\mathrm{\δ}}---(4-26)$

Here, $\mathrm{\ψ}=(1-v_c)r_0^{-\sqrt{\mathrm{\α}}}{d}_s\left(t\right)$

$c_4\left(r_0\right)=-\frac{\{(1-v_c)(\sqrt{\mathrm{\α}}-1)r_0^2+[1-v_c+\sqrt{\mathrm{\α}}(1+v_c)\left]b^2\right\}{\mathrm{\ψ}}^{\′}}{\mathrm{\δ}}---(4-27)$

Here, ${\mathrm{\ψ}}^{\′}=(1+v_c)r_0^{\sqrt{\mathrm{\α}}}{d}_s\left(t\right)$

$\begin{array}{c}\mathrm{\δ}=(1-v_c^2)(1-\sqrt{\mathrm{\α}})[{(a/r_0)}^{\sqrt{\mathrm{\α}}}{b}^2+{(r_0/a)}^{\sqrt{\mathrm{\α}}}{r}_0^2]\\ -[(1-v_c^2)+\sqrt{\mathrm{\α}}{(1+v_c)}^2]{(r_0/a)}^{\sqrt{\mathrm{\α}}}{b}^2\\ -[(1-v_c^2)+\sqrt{\mathrm{\α}}{(1-v_c)}^2]{(a/r_0)}^{\sqrt{\mathrm{\α}}}{r}_0^2\end{array}---(4-28)$

Formula (4-24)～(4-28) is substituted into formula (4-6), (4-3), (4-18) and (4-19) respectively, works as r₀With α When knowing, radial stress σ can be tried to achieve accordingly_r(r) and tangential stress σ_θ(r).

Due to being r at the position of crack tip₀, according to formula (4-3):

$\frac{e_{\mathrm{ef}}}{1-v_c^2}[(1+v_c)c_1\left(r_0\right)+\frac{(1-v_c)c_2\left(r_0\right)}{r_0^2}]=f_t---(4-29)$

R can be tried to achieve from formula (4-15) and (4-5)₀Place's tangential cracking strain

${\mathrm{\ϵ}}_{\mathrm{\θ}}^c\left(r_0\right)=\frac{u\left(r_0\right)}{r_0}=c_1\left(r_0\right)+\frac{c_2\left(r_0\right)}{r_0^2}---(4-30)$

Therefore, [a, r₀] in the range of averagely tangentially cracking strain be:

$\stackrel{\&overbar;}{{\mathrm{\ϵ}}_{\mathrm{\θ}}^c}=\frac{1}{r_0-a}{\&integral;}_a^{r_0}(c_1\left(\mathrm{\ξ}\right)+\frac{{\text{c}}_2\left(\mathrm{\ξ}\right)}{{\mathrm{\ξ}}^2})\mathrm{d\ξ}---(4-31)$

Equally, on cracking face, average tangential strain can be tried to achieve by formula (4-15) and (4-17)

$\begin{array}{c}\stackrel{\&overbar;}{{\mathrm{\ϵ}}_{\mathrm{\θ}}^c}=\frac{1}{r_0-a}{\&integral;}_a^{r_0}(c_3\left(r_0\right){\mathrm{\ξ}}^{(\sqrt{\mathrm{\α}}-1)}+c_4\left(r_0\right){\mathrm{\ξ}}^{(-\sqrt{\mathrm{\α}}-1)})\mathrm{d\ξ}\\ =\frac{(r_0^{\sqrt{\mathrm{\α}}}-a^{\sqrt{\mathrm{\α}}})[c_3\left(r_0\right)+c_4\left(r_0\right)/{\left(a{r}_0\right)}^{\sqrt{\mathrm{\α}}}]}{\sqrt{\mathrm{\α}}(r_0-a)}\end{array}---(4-32)$

Formula (4-31) and (4-32) are substituted in formula (4-8), the part that can ftracture concrete Stiffness degradation factor alpha

$\mathrm{\α}=\frac{f_t\exp \{-\mathrm{\γ}[(r_0^{\sqrt{\mathrm{\α}}}-a^{\sqrt{\mathrm{\α}}})[c_3\left(r_0\right)+c_4\left(r_0\right)/{\left(a{r}_0\right)}^{\sqrt{\mathrm{\α}}}]/\sqrt{\mathrm{\α}}(r_0-a)-\frac{1}{r_0-a}\mathrm{\χ}\left]\right\}}{\frac{e_{\mathrm{ef}}(r_0^{\sqrt{\mathrm{\α}}}-a^{\sqrt{\mathrm{\α}}})[c_3\left(r_0\right)+c_4\left(r_0\right)/{\left(a{r}_0\right)}^{\sqrt{\mathrm{\α}}}]}{\sqrt{\mathrm{\α}}(r_0-a)}}---(4-33)$

Here, $\mathrm{\χ}={\&integral;}_a^{r_0}(c_1\left(\mathrm{\ξ}\right)+\frac{c_2\left(\mathrm{\ξ}\right)}{{\mathrm{\ξ}}^2})\mathrm{d\ξ}$

Therefore, according to formula (4-29) and (4-33), it is possible to obtain r₀And α.

With the gradually development in crack, work as t=t₂When, crack progressing to concrete surface, concrete cover cylinder is complete Full rupture.At this moment, r in formula (4-29) and (4-33)₀=b, that is,

$\frac{e_{\mathrm{ef}}}{1-v_c^2}[(1+v_c)c_1\left(b\right)+\frac{(1-v_c)c_2\left(b\right)}{b^2}]=f_t---(4-34)$

$\mathrm{\α}=\frac{f_t\exp \{-\mathrm{\γ}[(b^{\sqrt{\mathrm{\α}}}-a^{\sqrt{\mathrm{\α}}})[c_3\left(b\right)+c_4\left(b\right)/{\left(\mathrm{ab}\right)}^{\sqrt{\mathrm{\α}}}]/\sqrt{\mathrm{\α}}(b-a)-\frac{1}{b-a}\mathrm{\ω}\left]\right\}}{\frac{e_{\mathrm{ef}}(b^{\sqrt{\mathrm{\α}}}-a^{\sqrt{\mathrm{\α}}})[c_3\left(b\right)+c_4\left(b\right)/{\left(\mathrm{ab}\right)}^{\sqrt{\mathrm{\α}}}]}{\sqrt{\mathrm{\α}}(b-a)}}---(4-35)$

Here, $\mathrm{\ω}={\&integral;}_a^b(c_1\left(\mathrm{\ξ}\right)+\frac{c_2\left(\mathrm{\ξ}\right)}{{\mathrm{\ξ}}^2})\mathrm{d\ξ}$

According to formula (4-34) and (4-35), the time t of concrete cover cylinder instant of complete cracking₂Can be determined.

When concrete cover cylinder instant of complete cracking, formula (4-16) is cylinder intrinsic displacement governing equation, but due to Boundary condition changes so that solving also different.Additionally, the solution of formula (4-16) can be expressed as:

$u\left(r\right)=c_5\left(r_0\right)r^{\sqrt{\mathrm{\α}}}+c_6\left(r_0\right)r^{-\sqrt{\mathrm{\α}}}---(4-36)$

Boundary condition needs to meet:

$c_5(1+v_c)b^{(\sqrt{\mathrm{\α}}-1)}-c_6(1-v_c)b^{(-\sqrt{\mathrm{\α}}-1)}=0---(4-37)$

$c_5{a}^{\sqrt{\mathrm{\α}}}+c_6{a}^{-\sqrt{\mathrm{\α}}}=d_s\left(t\right)---(4-38)$

From formula (4-37) and (4-38):

$c_5=\frac{(1-v_c)a^{\sqrt{\mathrm{\α}}}}{(1-v_c)a^{2\sqrt{\mathrm{\α}}}+(1+v_c)b^{2\sqrt{\mathrm{\α}}}}{d}_s\left(t\right)---(4-39)$

$c_6=\frac{(1+v_c)a^{\sqrt{\mathrm{\α}}}{b}^{2\sqrt{\mathrm{\α}}}}{(1-v_c)a^{2\sqrt{\mathrm{\α}}}+(1+v_c)b^{2\sqrt{\mathrm{\α}}}}{d}_s\left(t\right)---(4-40)$

Average tangential strain can be expressed as accordingly

$\begin{array}{c}\stackrel{\&overbar;}{{\mathrm{\ϵ}}_{\mathrm{\θ}}}=\frac{1}{b-a}{\&integral;}_a^b{\mathrm{\ϵ}}_{\mathrm{\θ}}\left(r\right)\mathrm{dr}\\ =\frac{1}{b-a}{\&integral;}_a^b(c_5{r}^{(\sqrt{\mathrm{\α}}-1)}+c_6{r}^{(-\sqrt{\mathrm{\α}}-1)})\mathrm{dr}\\ =\frac{(b^{\sqrt{\mathrm{\α}}}-a^{\sqrt{\mathrm{\α}}})[c_5+c_6/\left(\mathrm{ab}\right)\sqrt{\mathrm{\α}}]}{\sqrt{\mathrm{\α}}(b-a)}\end{array}---(4-41)$

Therefore, in formula (4-33), Stiffness degradation factor alpha is

$\mathrm{\α}=\frac{f_t\exp \{-\mathrm{\γ}[(b^{\sqrt{\mathrm{\α}}}-a^{\sqrt{\mathrm{\α}}})[c_5+c_6/{\left(\mathrm{ab}\right)}^{\sqrt{\mathrm{\α}}}]/\sqrt{\mathrm{\α}}(b-a)-\frac{1}{b-a}\mathrm{\ω}\left]\right\}}{\frac{e_{\mathrm{ef}}(b^{\sqrt{\mathrm{\α}}}-a^{\sqrt{\mathrm{\α}}})[c_5+c_6/{\left(\mathrm{ab}\right)}^{\sqrt{\mathrm{\α}}}]}{\sqrt{\mathrm{\α}}(b-a)}}---(4-42)$

Wherein, f_tThe tensile strength of concrete；Exp is exponential function form, i.e. function exp (x)=e^xSolution formula simultaneously (4-39), (4-40) and (4-42), can get c₅, c₆And α.

Work as c₅And c₆It is known that b point tangential strain can be tried to achieve by formula (4-36), that is,

${\mathrm{\ϵ}}_{\mathrm{\θ}}\left(b\right)=c_5{b}^{(\sqrt{\mathrm{\α}}-1)}+c_6{b}^{(-\sqrt{\mathrm{\α}}-1)}---(4-43)$

Therefore, surface crack width of concrete covers is

$w_c=2\mathrm{\πb}[{\mathrm{\ϵ}}_{\mathrm{\θ}}\left(b\right)-{\mathrm{\ϵ}}_{\mathrm{\θ}}^{e,m}\left(b\right)]---(4-44)$

In above formula,For maximum elastic strain at r=b, according to timoshenko and goodier, can express For:

${\mathrm{\ϵ}}_{\mathrm{\θ}}^{e,m}\left(b\right)=\frac{{\mathrm{\σ}}_{\mathrm{\θ},m}\left(b\right)-v_c{\mathrm{\σ}}_r\left(b\right)}{e_{\mathrm{ef}}}---(4-45)$

In formula, ε_{θ, m}B () is tangential strain maximum at r=b.Due to σ_r(b)=0 and ρ_{θ, m}(b)=f_t, therefore crack width Degree w_cIt is finally:

$\begin{array}{c}{w}_c=2\mathrm{\πb}[c_5{b}^{(\sqrt{\mathrm{\α}}-1)}+c_6{b}^{(-\sqrt{\mathrm{\α}}-1)}-\frac{f_t}{e_{\mathrm{ef}}}]\\ =\frac{4\mathrm{\π}{d}_s\left(t\right)}{(1-v_c){(a/b)}^{\sqrt{\mathrm{\α}}}+(1+v_c){(b/a)}^{\sqrt{\mathrm{\α}}}}-\frac{2\mathrm{\πb}{f}_t}{e_{\mathrm{ef}}}\end{array}---(4-46)$

From formula (4-46) as can be seen that calculating and the concrete component dimensional parameters a of concrete surface crack width, B, mechanical performance of concrete parameter f_t、e_c, concrete deformation performance parameter v_c、Solve with by Fracture Mechanics of Concrete is theoretical Crack impact Stiffness degradation factor alpha and and steel bar corrosion product thickness increase time-dependence function d_sT () is related, wherein d_s(t) with The parameters such as corrosion product quality, corrosion product type, corrosion product density, reinforcing bar density, corrosion electric current density are related.

Document li chunqing, melchers robert e and zheng jianjun.analytical model for corrosion-induced crack width in reinforced concrete structures[j].aci Structural journal, in 2006,103 (4): 479-487, partial parameters are given, c=31mm, d=12mm, d₀= 12.5 μm, e_ef=18.82gpa, f_t=5.725mpa, i_corr=0.3686ln (t)+1.1305 μ a/cm², α_rust=0.57, v_c =0.18, ρ_rust=3600kg/m³, ρ_st=7850kg/m³.

Document Zheng builds up the Army, the analytic solutions [j] of Zhou Xinzhu, li chun-qing. corrosion damage of reinforced concrete structures. water conservancy Journal, 2004, (12): in 1-9., define 5000 ＜ γ ＜ 10000, take γ=7500.

Analyzed by above-mentioned theory, it can be gathered that the calculating of concrete surface crack width and reinforcing steel corrosion rate theoretical model Flow process is:

(1) determine the basic parameter of reinforced concrete member, including bar diameter d, thickness of concrete cover c, coagulation Native tensile strength f_t, modulus of elasticity of concrete ec, concrete creep coefficientConcrete Poisson's ratio v_c, simultaneous formula (4-39), (4-40) steel bar corrosion product thickness d when and (4-42), can get concrete surface cracking_s(t) and concrete Stiffness degradation system The calculation relational expression of number α；

(2) utilize d_sT () and the relation of α, according to formula (4-46), can get concrete surface cracking width w_cWith reinforcing bar Corrosion product thickness d_sThe calculation expression of (t)；

(3) by d_sT () uses w_cRepresent, substitute in formula (4-1), steel bar corrosion product quality w can be finally given_rust(t) with Concrete surface cracking width w_cComputation model.

After the reinforcing bar in electrochemistry accelerated corrosion armored concrete test specimen, make surface of test piece that different in width to occur Crack (0.2mm, 0.4mm, 0.7mm and 1.0mm), according to concrete water-cement ratio, bar diameter, thickness of protection tier etc. because The impact to corrosion cracking for the element, verifies the reliability of the dependency relation of fracture width that present invention research obtains and reinforcing steel corrosion rate Property, and improved by the result of the test surveying reinforcing steel corrosion rate.

In the theoretical model of above-mentioned foundation, complex due to calculating, therefore, using in data of the present invention and document Data, simplifies to theoretical model, to meet the needs of practical engineering application.

In formula (4-46), concrete component dimensional parameters a, b, mechanical performance of concrete parameter f_t、e_c, concrete change Shape performance parameter v_c、Chosen all in accordance with engineering actual parameter, be utilized respectively Practical Project on-site concrete resilience resistance to compression Intensity and tensile strength, the relation of elastic modelling quantity, typically take that tensile strength is compression strength 1/10～1/12, concrete elastic Modulus and Creep Coefficient can refer to " highway reinforced concrete and prestressed concrete bridge contain design specification " (jtg d62-2004) The regulation of different concrete crushing strengths is chosen, concrete Poisson's ratio typically takes 0.18～0.20, rigidity is affected for crack Reduction coefficient α, according to the data in test data and document [32-34], has substituted into the tensile strength of concrete, the having of concrete Effect elastic model, bar diameter, concrete cover to reinforcement thickness parameter have obtained multigroup α numerical value, as shown in table 1.r₂Generation Coefficient correlation in table regression analysis, r²Closer to 1, represent that regression effect is better.Carry out returning using spss software and calculate, can Obtain:

α=0.01137638 × (t/365)^{(-2.198836253)}+0.1235655576(r²=0.974) (4-47)

Formula (4-47) is substituted into using in 4.2 built theoretical models, can get steel bar corrosion thickness d_sThe calculating mould of (t) Type, is shown below.

$d_s\left(t\right)=\frac{(w_c+\frac{2\mathrm{\πb}{f}_t}{e_{\mathrm{ef}}})\·[(1-v_c){(a/b)}^{\sqrt{\mathrm{\α}}}+(1+v_c){(b/a)}^{\sqrt{\mathrm{\α}}}]}{4\mathrm{\π}}---(4-48)$

Formula (4-48) is substituted in formula (4-1), can get reinforcing steel corrosion rate and concrete surface crack width, agent on crack resistance of concrete The related computing formula of the parameters such as tensile strength, elastic modelling quantity, bar diameter, thickness of concrete cover, as shown in formula (4-49).

$w_{\mathrm{rust}}\left(t\right)=\frac{(w_c+\frac{2\mathrm{\πb}{f}_t}{e_{\mathrm{ef}}})\·(d+2d_0)\·[(1-v_c){(a/b)}^{\sqrt{\mathrm{\α}}}+(1+v_c){(b/a)}^{\sqrt{\mathrm{\α}}}]}{4\·(\frac{1}{{\mathrm{\ρ}}_{\mathrm{rust}}}-\frac{{\mathrm{\α}}_{\mathrm{rust}}}{{\mathrm{\ρ}}_{\mathrm{st}}})}---(4-49)$

Convolution (4-47) and (4-49), you can reinforcing steel corrosion rate under different larval instar, different cracking width is calculated.

The multigroup α numerical value of table 1

With under three kinds of ratio of muds (0.3,0.4,0.5) factor, bar diameter be during 25mm as a example, concrete surface crack width Degree is as shown in Figure 4 with the relation test value of reinforcing steel corrosion rate, model calculation value and simplified model calculated value.

Figure 4, it is seen that compared with theoretical model calculated value, by simplifying the model calculation value obtaining and test value More closely, the relation of reinforcing steel corrosion rate and fracture width development can preferably be simulated.

In order to verify the built theoretical model of the present invention further, choose existing favour cloud tinkling of pieces of jade model, Highway house hair swallow respectively Model, " concrete structure durability evaluation criteria " (cecs220:2007) recommended models and andrade model and the present invention Built simplified mathematical model and test value are compared analysis.With the ratio of mud be 0.4, bar diameter as 12mm, concrete protective Thickness degree be during 40mm as a example, the relation test value of concrete surface crack width and reinforcing steel corrosion rate, the built simplification of the present invention Model calculation value, the contrast of model calculation value are as shown in Figure 5.

As seen from Figure 5, with the increase of fracture width, reinforcing steel corrosion rate constantly increases.Compared with test value, wherein Reinforcing steel corrosion rate all over-evaluated by favour cloud tinkling of pieces of jade model and Highway house's hair swallow model；" concrete structure durability evaluation criteria " (cecs220:2007) recommended models underestimate reinforcing steel corrosion rate；Andrade model underestimates reinforcing steel corrosion rate in early stage, and Stage has over-evaluated reinforcing steel corrosion rate；Compared with existing model, the present invention built simplified model computable value with test value has relatively Good meets.

Consider the impact of stirrup/distributing reinforcement

According to stirrup fracture carry out impact it is proposed that having or not stirrup in the case of, concrete surface crack width right Than computing formula:

Positioned at corner when:

Positioned at middle part when:

In formula (4-51) and (4-52), g is concrete shearing modulus,A represents The area that concrete is affected by stirrup, a=c s, wherein, c represents thickness of concrete cover, and s represents stirrup spacing；I= (1/12)s·c³；K=1.2 (takes square-section)；D is stirrup diameter；a_sv1Represent the sectional area of single hoop muscle, e_svFor stirrup Elastic modelling quantity.OrderThen have:

Positioned at corner when:

Positioned at middle part when:

Detect contrast with actual bridge member

Contrasted detection data during corrosive crack occurring in the studies above achievement and actual bridge structure, for verifying The applicability of the built theoretical model of the present invention.

Testing result contrasts with calculating

Example 1:

Cage bar is designed at guardrail positionDesign stirrupConcrete strength resilience Gong Wugece area, Each is surveyed area's measuring point number and is 16, and concrete carbonization depth have detected 2 measuring points, and each measuring point is all arranged by triangle disposition, mixes Solidifying protective soil layer thickness is surveyed area's number and is 3, and each is surveyed area and comprises 6 measuring points, and fracture width have chosen 3 of component middle part Measuring point.After testing, concrete strength resilience mean value is 33.2, and carbonation depth mean value is 0.46mm, according to " inspection by rebound method Concrete crushing strength technical regulation " (jgj/t 23-2011), after conversion, concrete strength is 27.8mpa；Concrete protective Layer thickness average value is 28.4mm；Fracture width mean value is 0.22mm；Damaged reinforcing bar length is 26.1cm；Damaged reinforcing bar is through table Weight of weighing after face rust cleaning dried process is 148.5g.

Built using the present invention and simplify theoretical model computing formula and consider that the rust distending that stirrup affects splits width correction meter Calculate formula, can be calculated reinforcing steel corrosion rate calculated value is 6.91%, and actually detected reinforcing steel corrosion rate is 7.72%, both Deviation is 10.45%.

Reinforcing bar is designed at floorings positionBidirectional arrangements, concrete strength resilience Gong Liugece area, each survey Area's measuring point number is 16, and concrete carbonization depth have detected 4 measuring points, and each measuring point is all arranged by triangle disposition, and concrete is protected Covering thickness is surveyed area's number and is 3, and each is surveyed area and comprises 3 measuring points, and fracture width have chosen 3 measuring points of component middle part. After testing, concrete strength resilience mean value is 35.0, and carbonation depth mean value is 0.2mm, according to " inspection by rebound method concrete Compression strength technical regulation " (jgj/t 23-2011), after conversion, concrete strength is 31.4mpa；Thickness of concrete cover Mean value is 22.5mm；Fracture width mean value is 0.08mm；Damaged reinforcing bar length is 36.4cm；Damaged reinforcing bar is through surface derusting Weight of weighing after dried process is 213.0g.

Built using the present invention and simplify theoretical model computing formula and consider that the rust distending that stirrup (distribution bar) affects splits Width correction computing formula, can be calculated reinforcing steel corrosion rate calculated value is 4.30%, and actually detected reinforcing steel corrosion rate is 5.09%, both deviations are 15.53%.

Example 2:

Box beam beam bottom position design cage bar φ 25, design stirrup φ 14 180, concrete strength resilience Gong Liugece area, often Ge Ce area measuring point number is 16, and concrete carbonization depth have detected 2 measuring points, and each measuring point is all arranged by triangle disposition, coagulation Protective soil layer thickness is surveyed area's number and is 3, and each is surveyed area and comprises 6 measuring points, and fracture width have chosen 3 surveys of component middle part Point.After testing, concrete strength resilience mean value is 44.0, and carbonation depth mean value is 0.15mm, according to " inspection by rebound method mixes Solidifying soil compression strength technical regulation " (jgj/t 23-2011), after conversion, concrete strength is 50.20mpa；Concrete protective Layer thickness average value is 25.9mm；Fracture width mean value is 0.17mm；Three measuring point Corrosion Reinforcement diameters are respectively 13.09mm、13.19mm、13.44mm.

Built using the present invention and simplify theoretical model computing formula and consider that the rust distending that stirrup affects splits width correction meter Calculate formula, can be calculated reinforcing steel corrosion rate calculated value is 9.20%, and actually detected reinforcing steel corrosion rate is 10.56%, two Person's deviation is 12.88%.

By the detection data to two actual three different parts of bridge structure in this section, considering stirrup impact On the basis of correction factor, the present invention is built rust distending and is split width with reinforcing steel corrosion rate simplification theoretical model calculated value respectively less than in fact Border detection data, the deviation at three positions is respectively 10.45%, 15.53% and 12.88%, therefore, can be according to Practical Project warp Test, calculated value is adopted with 1.05～1.15 correction factor, the needs of Practical Project Fast nondestructive evaluation technology can be met.

The present invention first steel bar corrosion is caused concrete surface crack carry out analysis of Influential Factors on the basis of, in conjunction with Concrete material mechanics and theory of elastic mechanics, establish the theory obtaining reinforcing steel corrosion rate using concrete surface crack width Computation model, the index such as main inclusion bar diameter, thickness of concrete cover, concrete tensile strength in this theoretical model. Because built theoretical calculation model is complex, therefore, by certain experimental study to the relevant parameter in this theoretical model Carry out simplification process.By showing with having model calculation value both at home and abroad and contrasting, the built simplified mathematical model of the present invention can be more Good is simulated to test value.On this basis it is proposed that a set of for actual field Dynamic Non-Destruction Measurement method, by with The contrast of Practical Project detection data, considers the impact that stirrup (distribution bar) fracture is carried out simultaneously, demonstrates this simplification reason Applicability by model.

Instant invention overcomes traditionally carrying out the derivation of equation only with test data, there is no theory as foundation, deriving Formula restricted application problem, the steel bar corrosion derived based on the mechanics of materials and rational mechanics and test data etc. The formula of degree Non-Destructive Testing, the model of half that the present invention derives has theory as foundation, and the scope of application is more extensive.

Although embodiment of the present invention is disclosed as above, it is not restricted to listed in specification and embodiment With, it can be applied to various suitable the field of the invention completely, for those skilled in the art, can be easily Realize other modification, therefore under the universal being limited without departing substantially from claim and equivalency range, the present invention does not limit In specific details with shown here as the legend with description.

Claims (8)

1. steel bar corrosion degree lossless detection method after a kind of reinforced concrete member corrosion is ftractureed is it is characterised in that include as follows Step:

Step one, be based on the mechanics of materials and rational mechanics, obtain equation below (4-49),

$w_{rust}\left(t\right)=\frac{(w_c+\frac{2{\mathrm{\πbf}}_t}{e_{ef}})\·(d+2d_0)\·\[(1-{\mathrm{\ν}}_c){(a/b)}^{\sqrt{\mathrm{\α}}}+(1+{\mathrm{\ν}}_c){(b/a)}^{\sqrt{\mathrm{\α}}}\]}{4\·(\frac{1}{{\mathrm{\ρ}}_{rust}}-\frac{{\mathrm{\α}}_{rust}}{{\mathrm{\ρ}}_{st}})}---(4-49)$

Wherein, e_efFor concrete effective modulus of elasticity, d is bar diameter, f_tFor concrete tensile strength, d₀For reinforcing bar and coagulation The thickness of concrete pore endless belt, ν between native bonding interface_cFor concrete Poisson's ratio, c is thickness of concrete cover, a=(d +2d₀)/2, b=c+ (d+2d₀)/2, α is concrete Stiffness degradation coefficient, ρ_rustFor corrosion product density, ρ_stFor reinforcing bar density, And α_rustIt is the coefficient related to corrosion product type；

Step 2, the fracture width w of measurement reinforced concrete member_cValue, is calculated corrosion product quality using formula (4-49) w_rustT () value, calculates the steel bar corrosion degree of this reinforced concrete member, afterwards to judge the security of this reinforced concrete member Energy.

2. steel bar corrosion degree lossless detection method after reinforced concrete member corrosion cracking as claimed in claim 1, its feature It is, in described step 2, if stirrup is located at the corner of this reinforced concrete member, being calculated according to equation below (4-51) has Quality w of steel bar corrosion product during stirrup_{There is stirrup},

Wherein, w_{No stirrup}It is corrosion product quality w being obtained according to formula (4-49)_rust(t) value, (ea)_sv=e_sva_sv,

E is the elastic modelling quantity of stirrup, l_svFor stirrup length on member section, g is concrete shearing modulus,A represents the area that concrete is affected by stirrup, a=c s, and wherein, c represents coagulation Protective soil layer thickness, s represents stirrup spacing, i=(1/12) s c³, k=1.2, d are stirrup diameter, a_sv1Represent single hoop muscle Sectional area, a_svRepresent the sectional area of all stirrups, e_svElastic modelling quantity for stirrup.

3. steel bar corrosion degree lossless detection method after reinforced concrete member corrosion cracking as claimed in claim 2, its feature It is, orderThen have:

4. steel bar corrosion degree lossless detection method after reinforced concrete member corrosion cracking as claimed in claim 1, its feature It is, in described step 2, if stirrup is located at the middle part of this reinforced concrete member, being calculated according to equation below (4-52) has Quality w of steel bar corrosion product during stirrup_{There is stirrup},

Wherein, w_{No stirrup}It is corrosion product quality w being obtained according to formula (4-49)_rust(t) value, (ea)_sv=e_sva_sv,

E is the elastic modelling quantity of stirrup, l_svFor stirrup length on member section, g is concrete shearing modulus,A represents the area that concrete is affected by stirrup, a=c s, and wherein, c represents coagulation Protective soil layer thickness, s represents stirrup spacing, i=(1/12) s c³, k=1.2, d are stirrup diameter, a_sv1Represent single hoop muscle Sectional area, a_svRepresent the sectional area of all stirrups, e_svElastic modelling quantity for stirrup.

5. steel bar corrosion degree lossless detection method after reinforced concrete member corrosion cracking as claimed in claim 4, its feature It is, orderThen have:

6. steel bar corrosion degree lossless detection method after described reinforced concrete member corrosion cracking as arbitrary in claim 1 to 5, It is characterized in that, in described step one, the detailed process obtaining formula (4-49) includes:

(1.1) it is based on the mechanics of materials and rational mechanics, swollen for the rust of concrete cover crack and damage influence area is reduced to sky Between axisymmetric thick cyclinder, then have,

The internal-and external diameter of concrete cover thick cyclinder is respectively as follows:

A=(d+2d₀)/2, b=c+ (d+2d₀)/2；

Corrosion product thickness d_sT () is:

$d_s\left(t\right)=\frac{w_{rust}\left(t\right)}{\mathrm{\π}(d+2d_0)}(\frac{1}{{\mathrm{\ρ}}_{rust}}-\frac{{\mathrm{\α}}_{rust}}{{\mathrm{\ρ}}_{st}})---(4-1)$

(1.2) determine the basic parameter value of reinforced concrete member, including bar diameter d, thickness of concrete cover c, coagulation Native tensile strength f_t, concrete Poisson's ratio ν_c, simultaneous formula (4-39), (4-40) and (4-42), c can be tried to achieve₅, c₆And α；)

$c_5=\frac{(1-{\mathrm{\ν}}_c)a^{\sqrt{\mathrm{\α}}}}{(1-{\mathrm{\ν}}_c)a^{2\sqrt{\mathrm{\α}}}+(1+{\mathrm{\ν}}_c)b^{2\sqrt{\mathrm{\α}}}}{d}_s\left(t\right)---(4-39)$

$c_6=\frac{(1+{\mathrm{\ν}}_c)a^{\sqrt{\mathrm{\α}}}{b}^{2\sqrt{\mathrm{\α}}}}{(1-{\mathrm{\ν}}_c)a^{2\sqrt{\mathrm{\α}}}+(1+{\mathrm{\ν}}_c)b^{2\sqrt{\mathrm{\α}}}}{d}_s\left(t\right)---(4-40)$

$\mathrm{\α}=\frac{f_t\exp \{-\mathrm{\γ}\[(b^{\sqrt{\mathrm{\α}}}-a^{\sqrt{\mathrm{\α}}})\[c_5+c_6/{\left(ab\right)}^{\sqrt{\mathrm{\α}}}\]/\sqrt{\mathrm{\α}}(b-a)-\frac{1}{b-a}\mathrm{\ω}\]\}}{\frac{e_{ef}(b^{\sqrt{\mathrm{\α}}}-a^{\sqrt{\mathrm{\α}}})\[c_5+c_6/{\left(ab\right)}^{\sqrt{\mathrm{\α}}}\]}{\sqrt{\mathrm{\α}}(b-a)}}---(4-42)$

Wherein γ is concrete material constant；

(1.3) utilize the c obtaining in step (1.2)₅, c₆And α, according to formula (4-46), obtain the crack of concrete surface cracking Width w_cWith steel bar corrosion product thickness d_sThe calculation expression of (t)；

$\begin{array}{c}{w}_c=2\mathrm{\π}b\[c_5{b}^{(\sqrt{\mathrm{\α}}-1)}+c_6{b}^{(-\sqrt{\mathrm{\α}}-1)}-\frac{f_t}{e_{ef}}\]\\ =\frac{4{\mathrm{\πd}}_s\left(t\right)}{(1-{\mathrm{\ν}}_c){(a/b)}^{\sqrt{\mathrm{\α}}}+(1+{\mathrm{\ν}}_c){(b/a)}^{\sqrt{\mathrm{\α}}}}-\frac{2{\mathrm{\πbf}}_t}{e_{ef}}\end{array}---(4-46)$

(1.4) simultaneous formula (4-1) and (4-46), obtains steel bar corrosion product quality w_rust(t) and concrete surface cracking width w_cCalculation expression formula (4-49).

7. steel bar corrosion degree lossless detection method after reinforced concrete member corrosion cracking as claimed in claim 6, its feature It is, in described step (1.2), obtain multigroup numerical value of concrete Stiffness degradation factor alpha according to formula (4-42), then sharp again Carried out with spss software returning and calculate, obtain equation below (4-47),

α=0.01137638 × (t/365)^{(-2.198836253)}+0.1235655576(r²=0.974) (4-47)

Calculate the reinforced concrete member under different larval instar and different fracture width using formula (4-47) and formula (4-49) Reinforcing steel corrosion rate.

8. steel bar corrosion degree lossless detection method after reinforced concrete member corrosion cracking as claimed in claim 6, its feature It is, in described step (1.2),e_cRepresent 28 days elastic modelling quantity of concrete,For concrete creep system Number.