CN114091307A - Method and system for analyzing concrete humidity field and shrinkage stress field - Google Patents
Method and system for analyzing concrete humidity field and shrinkage stress field Download PDFInfo
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Abstract
The invention discloses an analysis method and a system for a concrete humidity field and a shrinkage stress field, which comprises the steps of obtaining relative humidity data, constructing a relative humidity equation based on the relative humidity data, solving the relative humidity equation to obtain relative humidity, and calculating the relative humidity to obtain shrinkage strain; and acquiring elastic strain and creep strain, constructing a stress time course analysis formula based on the shrinkage strain, the elastic strain and the creep strain, and calculating by using the stress time course analysis formula to obtain the analysis results of the concrete humidity field and the shrinkage stress field. The invention fully considers the coupling relation between the relative humidity and the shrinkage strain, and finally accurately analyzes the stress of the reinforced concrete structure under the shrinkage action on the premise of the creep action.
Description
Technical Field
The invention relates to the technical field of concrete stress analysis, in particular to a method and a system for analyzing a concrete humidity field and a shrinkage stress field.
Background
The shrinkage deformation of concrete mainly comprises three parts of drying shrinkage deformation and self-shrinkage deformation caused by humidity change, the self-shrinkage of the concrete, particularly the quantitative calculation of the self-shrinkage deformation, is rarely researched at present, and related data at home and abroad are rarely related. At present, the research on the drying shrinkage deformation of concrete is relatively more, and when the relative humidity of the external environment is lower, the concrete diffuses moisture to the external environment, so that the drying shrinkage deformation is caused. The magnitude of the drying shrinkage distortion is affected by two aspects: firstly, receive the influence of the inside moisture loss volume of concrete, secondly receive the influence of the inside humidity gradient of concrete. The uneven diffusion rate of water inside and outside the concrete can cause a humidity gradient to be formed inside the concrete, thereby causing the shrinkage of the concrete, particularly on the surface of the concrete, the humidity gradient is extremely large, and the surface crack of the concrete is easily caused. Compared with a temperature field and a temperature stress field, the humidity field and the induced shrinkage stress field are rarely researched, and the main reason is that in a concrete material, the humidity conduction speed is about 1000 times smaller than that of temperature conduction, the humidity changes very slowly, when the drying depth reaches 7cm, the drying depth needs one month, and when the drying depth reaches 70cm, the drying depth needs nearly ten years, so that the influence of the humidity change on the structure is ignored in many researches; secondly, because of the numerous factors that influence the calculation parameters and boundary conditions of the humidity field and the drying stress field inside the concrete, it is very difficult to obtain exact and reasonable values thereof, and thus it is difficult to describe the drying shrinkage and the drying stress properly.
Disclosure of Invention
In order to solve the problem that the influence of a humidity field on the shrinkage deformation of the concrete is not considered, the final stress analysis is inaccurate and the like in the prior art, the invention provides an analysis method and system for the humidity field and the shrinkage stress field of the concrete.
In order to achieve the technical purpose, the invention provides an analysis method for a concrete humidity field and a shrinkage stress field, which specifically comprises the following steps:
acquiring relative humidity data, constructing a relative humidity equation based on the relative humidity data, solving the relative humidity equation to obtain relative humidity, and calculating the relative humidity to obtain shrinkage strain;
and acquiring elastic strain and creep strain, constructing a stress time course analysis formula based on the shrinkage strain, the elastic strain and the creep strain, and calculating by using the stress time course analysis formula to obtain the analysis results of the concrete humidity field and the shrinkage stress field.
Optionally, the relative humidity data includes an evaporation diffusion drying relative humidity variation and a self-drying relative humidity variation, wherein the evaporation diffusion drying relative humidity variation is obtained by performing diffusion law calculation, and the self-drying relative humidity variation is obtained by performing hydration degree calculation.
Optionally, the process of solving the humidity equation includes:
constructing boundary conditions, wherein the boundary conditions are concrete surface humidity boundary conditions, absolute humidity boundary conditions and concrete boundary conditions exposed in air;
and solving the humidity equation by a finite element method based on the boundary condition to obtain the relative humidity.
Optionally, the process of calculating the relative humidity includes:
and calculating the relative humidity by constructing a relation between the shrinkage strain and the relative humidity to obtain the shrinkage strain, wherein the ratio of the shrinkage strain to the relative humidity is a shrinkage coefficient, and the shrinkage coefficient is obtained by calculating the final shrinkage strain.
Optionally, the process of constructing the stress time course analysis formula includes:
solving the shrinkage strain, the elastic strain and the creep strain to obtain a stress formula, constructing a stress time course analysis formula by integrating with the section curvature based on the stress formula,
the system comprises a base, a tension sensor, a sensor and a controller, wherein the elastic strain is obtained by calculation based on the Huke's law, the creep strain comprises basic creep strain and dry creep strain, the dry creep strain is obtained by calculation based on a dry creep calculation formula, and the basic creep strain is obtained by the calculation of the elastic strain correlation.
In order to better achieve the above object, the present invention further provides an analysis system for a concrete humidity field and a shrinkage stress field, comprising:
the processing module is used for acquiring relative humidity data, constructing a relative humidity equation based on the relative humidity data, solving the relative humidity equation to obtain relative humidity, and calculating the relative humidity to obtain shrinkage strain;
the solving module is used for obtaining elastic strain and creep strain, constructing a stress time course analysis formula based on the shrinkage strain, the elastic strain and the creep strain, and calculating through the stress time course analysis formula to obtain an analysis result of the concrete humidity field and the shrinkage stress field.
Optionally, in the processing module, the relative humidity data includes an evaporation diffusion drying relative humidity variation and a self-drying relative humidity variation, wherein the evaporation diffusion drying relative humidity variation is obtained by performing diffusion law calculation, and the self-drying relative humidity variation is obtained by performing hydration degree calculation.
Optionally, the processing module includes: the first processing unit is used for constructing boundary conditions, wherein the boundary conditions are concrete surface humidity boundary conditions, absolute humidity boundary conditions and concrete boundary conditions exposed to air;
and the second processing unit solves the humidity equation by a finite element method based on the boundary condition to obtain the relative humidity.
Optionally, the processing module further includes: and the third processing unit calculates the relative humidity by constructing a relation between the shrinkage strain and the relative humidity to obtain the shrinkage strain, wherein the ratio of the shrinkage strain to the relative humidity is a shrinkage coefficient, and the shrinkage coefficient is obtained by calculating the final shrinkage strain.
Optionally, the solving module includes: the first solving unit is used for solving shrinkage strain, elastic strain and creep strain to obtain a stress formula;
the second solving unit is based on a stress formula and is integrated with the section curvature to construct a stress time-course analysis formula;
the elastic strain is obtained by calculation based on the Hooke's law, the creep strain comprises basic creep strain and dry creep strain, the dry creep strain is obtained by calculation based on a dry creep calculation formula, and the basic creep strain is obtained by correlation calculation of the elastic strain.
The invention has the following technical effects:
the invention provides the generation of stress after the shrinkage generated at a certain point in the concrete due to drying and self-drying is restrained, and the development rule of the restrained stress under the combined action of the creep effect is considered, so that the shrinkage stress field at any moment is given, on the basis, the time-course analysis is carried out on the stress-strain change condition caused by the restrained shrinkage of the reinforced concrete structure, the respective calculation formulas of the concrete stress and the strain at any point on any moment and section and the stress expression of the reinforcing steel bar at any moment are deduced, and the concrete stress, the strain result and the reinforcing steel bar stress result can be accurately calculated according to the calculation formulas and the expressions.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a schematic flow chart of a method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a unit abstraction model according to an embodiment of the present invention;
fig. 3 is a schematic diagram of a system according to a second embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, the present invention provides a method for analyzing a concrete humidity field and a shrinkage stress field, which specifically provides the following contents:
before the concrete sets and hardens, shrinkage is considered to be free deformation, otherwise known as unconstrained deformation, since strength has not yet developed, and the deformation does not generate internal forces. When the strength of the concrete begins to develop continuously after the concrete is solidified and hardened, the adhesive force between the structure and the adjacent boundary or between the concrete and the internal reinforcing steel bars or embedded parts and the like also begins to be formed, the conditions of external constraint and self constraint of the concrete are met, and if the concrete shrinks, the deformation is bound by the limiting action of the internal constraint and the external constraint, so that the shrinkage stress is generated. Therefore, the shrinkage stress is generated by the shrinkage of the concrete under the action of the external boundary and the internal self-constraint, and the deformation and the constraint are both indispensable, wherein the generation of the constraint is a prerequisite for the deformation to cause the internal force.
The establishment of the shrinkage stress of concrete is complicated mainly by the non-linear relationship between shrinkage stress and strain. For early concretes, the key to the establishment of the shrinkage stress field is the establishment of the stress-strain constitutive relation of early concretes. However, unlike the mature structure, the constitutive relation of early concrete has the characteristics of nonlinearity and timeliness. The non-linearity is mainly due to the fact that concrete is an elastoplastic body, which, in addition to elastic deformation, also interacts with the shrinkage effect and creep effect. The timeliness mainly means that various material parameters of early concrete are in continuous change development and do not tend to be stable, so that the elasticity modulus, the strength, the poisson ratio, the (relative) humidity and the like are functions of time and are not constants. From the above analysis, it is found that shrinkage and creep are major contributing factors of stress in early concrete, and both vary considerably even in a relatively short period of time, and therefore, sufficient attention must be paid.
For early shrinkage of concrete, the total deformation εtotalBy elastic deformation epsilonelContraction deformation epsilonshAnd creep deformation εcThe three parts are shown in the formula (3-1).
εtotal＝εel+εsh+εc (3-1)
The following are analyzed one by one:
first, elastic deformation epsilonelCan be determined by Hooke's law;
good and shrinkage deformation epsilonshMainly including temperature caused by temperature changesShrinkage distortion and drying shrinkage distortion epsilon caused by humidity changedshAnd self-contraction deformation epsilonashThree parts. Only the shrinkage caused by humidity changes is considered here, so that it comprises only two parts, drying shrinkage and self-shrinkage.
The creep and the creep are greatly influenced by the dry environment and generally consist of two parts, namely basic creep and dry creep. The basic creep is the creep generated by the structural component under the condition of no humidity exchange with the outside, and is also the real creep. The dry creep is the change of the creep of the structural member caused by the change of humidity in a dry environment, i.e. the residual parts after elastic deformation, shrinkage deformation and basic creep are deducted from the total deformation, and the creep effect of limited stress increment caused by shrinkage increment is substantially the creep effect, which is greatly influenced by the shrinkage of the concrete and is an important parameter for early concrete. In the calculation process, the basic creep and the dry creep are calculated separately. Wherein, the basic creep is composed of two parts of elastic creep and incremental creep, and is directly related to the instantaneous elastic strain through a creep coefficient and an age adjustment coefficient (namely an aging coefficient); the creep-drying is related to many factors such as relative humidity and microcracking effect, and is described herein using the simple equation of the creep-drying model proposed by Bazant. The implementation of this early stress field is derived from a detailed analysis below.
Derivation process of concrete stress increment, namely how to calculate and obtain stress formula
Let t be t0The concrete is internally restrained by shrinkage to generate an initial shrinkage limited stress sigma0(t0) (usually tensile stress), an initial elastic tensile strain ε (t) is generated therefrom0)＝σ0(t0)/Et0And shrinkage strain epsilonsh(t0) And (5) instantaneously balancing. Thereafter, the concrete will creep under this compressive stress, relaxing the compressive stress, so that the compressive tensile stress at that point is reduced. Shrinkage and creep are inter-related and difficult to distinguish unambiguously. However, for the purpose of theoretical derivation, the dry creep is calculated below as a single term. In harvestingThe initial limited stress sigma of the point under the combined action of shrinkage and creep0(t0) Passing through t-t0After time, a stress increment delta sigma will be formed0(t0T), which in turn, like the initial constrained stress, will produce a corresponding creep and contraction, which is repeated, constantly changing the stress state at that point.
Also, this analysis process can be generalized to a more general case, for which the incremental expression Δ σ of the stress at a certain point inside the concrete under the combined action of shrinkage and creep is derived.
Let t be t0At that moment, the stress at a certain point inside the concrete is σ (t)0) Then the strain is ε (t)0)＝σ0(t0)/E(t0) Under the continuous action of contraction and creep, the stress increment is delta sigma (t) after the time delta t to the time t0T). Then t0Delta strain delta [ epsilon ] (t) over time period t0T) is calculated as the following formula (3-2):
Δεtotal(t0,t)＝Δεe(t0,t)+Δεsh(t0,t)+Δεbc(t0,t)+Δεdc(t0,t) (3-2)
in the formula,. DELTA.epsilontotal(t0T) is t0Total strain increase delta epsilon of a certain point in the concrete within t time periode(t0T) is t0And (3) calculating the elastic strain increment of a certain point in the concrete in the time period t according to the formula (3-3):
in the formula E (t)0) Is t0Time of day modulus of elasticity, Δ ε, of concretesh(t0T) is t0The shrinkage strain increment of a certain point in the concrete in the time period t is composed of a drying shrinkage part and a self-shrinkage part (both are functions of humidity), and the formula is (3-4):
Δεsh(t0,t)＝Δεds(t0,t)+Δεas(t0,t) (3-4)
in the formula,. DELTA.. di-elect consds(t0T) is t0Increase of drying shrinkage of a point in the concrete within a time period of tas(t0T) is t0And (4) self-contraction increment of a certain point in the concrete within the time period t.
Δεbc(t0T) is t0Basic creep strain at a point in the concrete within a time period of t, due to elastic creep Δ εec(t0T) and incremental creep Δ εic(t0T) two parts, namely:
Δεbc(t0,t)＝Δεec(t0,t)+Δεic(t0,t) (3-5)
in the formula (I), the compound is shown in the specification,
is t0Creep coefficient of concrete at time t, χ (t)0T) is the age adjustment factor of the concrete, generally 0.5<χ(t0,t)<1, and usually 0.8 may be desirable.
Δεdc(t0T) is t0The dry creep increase at a certain point in the concrete in the time period t can be calculated by using a dry creep calculation formula proposed by Bazant.
Substituting the formulas (3-3), (3-6) and (3-7) into the formula (3-2) can obtain:
namely:
since the strain increase caused by concrete shrinkage and creep is 0 under limited conditions, the following formula is given:
thus, it is possible to obtain:
in the formula (I), the compound is shown in the specification,
is the equivalent modulus of elasticity.
The above formula is that the concrete is at a certain point inside the concrete from the initial time t0Begin to experience Δ t-t under the combined action of contraction and creep0The following stress increment expression, whereby the stress at time t can be obtained by:
σ(t)＝σ(t0)+σ(t0,t) (3-12)
delta sigma (t) obtained from (3-11)0T) is Δ t ═ t-t0The average stress increment generated in the period can theoretically obtain the stress at the moment t, but the stress at the moment t can be obtained0Stress at any time between t can only be at delta sigma (t)0) Roughly estimated within the range of Δ σ (t). If we want to get the accurate value, we can narrow the time interval Δ t infinitely, i.e. Δ t → 0, we can get t0Stress at time σ (t)0) Instant increment of delta sigma (t)0τ) (stress infinitesimal), the expression of which is given by the following formula (3-13)
The early limited shrinkage stress of concrete is analyzedAnd (4) obtaining a corresponding incremental expression in the process of expansion, so that the stress value at any moment can be obtained theoretically. In general, the initial stress σ (t) is for the case of no external load at an early stage0) Is zero. Note that, in the above analysis, we assume that parameters relating to shrinkage, elastic modulus, creep, and the like are known, and in the above formula, the elastic strain and the creep strain are known through the above calculation, and the shrinkage strain is solved through the following steps.
And (3) analyzing the early humidity field of the concrete to construct a relative humidity equation:
concrete early relative humidity change composition analysis, namely, conceptionally constructing relative humidity equation
The internal humidity of early concrete is different from the external humidity, and internal moisture diffuses to the outside, so that the internal relative humidity changes, namely, the drying action, are caused; on the other hand, due to the hydration of the cementing material in the concrete, the water in the capillary pores is consumed, and even if the concrete does not lose water to the outside, the relative humidity in the concrete is also reduced to a certain extent, namely, the concrete is self-dried. Since drying and self-drying effects will cause a change in the Relative Humidity (RH) inside the concrete, determining the relative humidity field inside the concrete is a prerequisite for evaluating the shrinkage of the concrete.
In general, the humidity change caused by drying is not uniform along the interface, and from the outside to the inside, the humidity change is quicker as the humidity is closer to the surface layer; whereas the humidity variation resulting from the drying action can be considered uniform along the cross section. The relative humidity change quantity delta h of a certain point in the concrete consists of two parts:
Δh＝Δhd+Δhs (3-15)
wherein, Delta h is the total relative humidity change quantity of a certain point in the concrete, and Delta hdThe Δ h is the relative humidity change due to the internal self-drying effect.
The change of the concrete relative humidity with time can be expressed as:
in the formula (I), the compound is shown in the specification,
the total relative humidity change rate of a certain point in the concrete, the relative humidity change rate caused by drying and the relative humidity change rate caused by self-drying are respectively.
Calculating the change rate of the relative humidity caused by drying, namely calculating the change amount of the relative humidity of the evaporation diffusion drying
By using a classical model of concrete moisture diffusion, the relational expression of the water content in concrete versus the relative humidity migration is:
wherein w is the water content, t is the age, h is the relative humidity in the pores, C is the water permeability coefficient depending on h, the change of the parameter C needs to be determined by the drying test of the concrete, and the C is generally considered to decrease along with the decrease of the relative humidity in the material.
The adsorption and desorption isotherms are expressed as w ═ g (h), then:
in the formula (I), the compound is shown in the specification,
g' (h) represents the water-containing capacity (desorption isotherm slope). From the experimental results, g' (h) can be assumed to be constant k, yielding a nonlinear diffusion equation:
according to the law of diffusion(Fick's second law) can be expressed in the following form[7]：
Wherein d (h) is a humidity diffusion coefficient, and d (h) k · c (h).
The humidity diffusion coefficient D (h) is obviously influenced by ambient temperature and humidity conditions, can be generally fitted through experiments, and has a plurality of expression forms. It is generally expressed as a function of the relative humidity of the pores as set forth in the CEB-FIP (1990) specification:
in the formula, D1The maximum value of the humidity diffusion coefficient under the concrete saturation state (H ═ 1), HcIs D (h) 0.5D1The relative pore humidity, alpha and n, is a test constant.
The relative humidity change rate caused by self-drying is calculated
About
At present, a mature theoretical expression in this aspect does not exist, but the expression can be directly obtained through a pore relative humidity test of a test piece under a corresponding concrete closed condition, namely, the corresponding expression is determined by regression analysis according to a fitting curve of a test result. An empirical formula of autogenous shrinkage is obtained by analyzing and processing a large amount of experimental data, but the calculation error of the autogenous shrinkage of the early concrete is large. The concept of hydration was used in describing the properties of early concretes, and the change in humidity as the interior self-dries was calculated from the degree of hydration:
in the formula,. DELTA.hs(t)The humidity reduction value due to self-drying at age t, α and b are constants determined by experiments, and α (t) is the hydration degree at age t, which can be expressed based on the heat of hydration during the hydration reaction.
Expression of total relative humidity change rate and boundary condition
The formula (3-20) is substituted into the formula ((3-16):
the relative humidity of a certain point in the concrete can be calculated by the formula, and the analytic solution can be carried out by a finite element method and combining boundary conditions.
The boundary conditions of the humidity field can be classified into the following three categories:
first-class boundary conditions for which concrete surface humidity is a known function of time:
h(x,y,z,t)＝f(x,y,z,t) (3-24)
the second type of moisture-insulating boundary condition is as follows:
third class boundary conditions for concrete exposed to air:
wherein f (x, y, z, t) is a known function over time,
is the humidity gradient on the drying surface along the boundary unit normal, hsIs the relative humidity of the surface, heIs the ambient relative humidity, and f is the surface moisture exchange coefficient. The surface water exchange coefficient is the surface humidity transfer coefficient, which is related to the water cement ratio of concrete, the difference of internal surface humidity, temperature, wind speed and other factors, especially waterThe ash ratio and wind speed have a significant effect on the surface moisture exchange coefficient. The improved Menzel equation proposed by Yuan et al is generally considered to be in good agreement with the actual situation:
f(h-he)＝A(0.253+0.06Vα)(h-he) (3-27)
wherein A is an empirical coefficient and depends on factors such as concrete water cement ratio, and VαIs the average wind speed (in m/s), heIs the ambient relative humidity. However, when there is no test data, it is preferably 5X 10-3m2/d。
Control equation for macroscopic humidity in cast-in-place concrete
The control equation for macroscopic humidity from Fick's second law and conservation of humidity is as follows:
wherein h (x, y, z, t) is the relative humidity distribution, kx、ky、kzThe coefficients of humidity diffusion in three dimensions are respectively, and if the humidity diffusion is considered to be isotropic, k can be expressedx、ky、kzAre simplified to D (h);
the rate of loss from dry relative humidity is caused by the consumption of water by the concrete gel hydration reaction, and its value depends mainly on the properties of the compound itself.
The above-mentioned contents are based on the principle of diffusion law, and establish the early relative humidity field of concrete, so that it can prepare for the conversion of relative humidity change into shrinkage caused by it, and this is also the precondition of concrete shrinkage stress field analysis.
Calculating the coupling of early shrinkage and relative humidity of concrete, namely calculating the relative humidity to obtain shrinkage strain
Since the shrinkage of concrete is closely related to the relative humidity in its pores, it is possible to build up the shrinkage εshThe amount of shrinkage is calculated from the relationship between the relative humidity hThe size of (2). According to the study of Bazant,. epsilonshThe relationship between h and h is as follows:
εsh＝kshh (3-29)
in the formula, kshIn order to be a coefficient of shrinkage,
in order to achieve the final shrinkage,
is the ratio of the modulus of elasticity at time t to the initial modulus of elasticity, fs(h) In the absence of demonstration of experimental results, the implications are not clear and can be calculated with reference to the following two formulae:
fs(h)＝1-h3 (3-31)
fs(h)＝1-h (3-32)
substituting the formula (3-32) into the formula (3-30) to obtain:
substituting (3-33) into (3-29) yields:
namely:
the above formula is a relational expression of free shrinkage and relative humidity, and the shrinkage at any time at any point in the concrete can be theoretically estimated by combining a calculation formula of a humidity field in the concrete.
Reinforced concrete structure shrinkage stress analysis
The reinforcing steel bars and the concrete are coordinated and work together through bonding force, and under the combined action of shrinkage and creep, the stress state of the reinforcing steel bars is changed while the internal stress state of the concrete is changed. In the cast-in-place reinforced concrete structure, under the combined action of the drying action of the surrounding external environment and the internal self-drying, the concrete is subjected to shrinkage deformation, the deformation generates shrinkage stress under the limitation of ortho-position constraint or internal self-constraint, and under the action of creep, the concrete and the deformation jointly change the internal stress state of the concrete. The stress time course analysis method of the reinforced concrete structure under the shrinkage effect in consideration of the creep effect under the general condition (i.e., from any given time regardless of the presence or absence of the external load) will be discussed below.
The unit abstraction model shown in fig. 2 was chosen for analysis. FIG. 2 shows a ribbed panel of thickness b, analyzed in unit width. The unit abstract model is relatively representative, and can be considered as a representative of a foundation slab, a pavement slab, a floor slab which is not yet demolded, a roof slab in use, and the like.
Stress time course analysis of structure in shrinkage limited state
The external load on the unit can be equivalently converted into an equivalent axial force N acting at a reference point 0eqAnd equivalent bending moment MeqThen at t0At time, instant strain ε at reference point 00(t0) And the cross-sectional curvature ψ (t) at this time0) The following relationship exists between the equivalent load and the load:
wherein A is the area of the equivalent cross section; b is the first moment of the equivalent section relative to the horizontal axis passing through the 0 point; i is a second moment of the equivalent section relative to a horizontal axis passing through a 0 point; ec(t0) Is t0Time of day the modulus of elasticity of the concrete.
t0Instantaneous strain and stress of concrete section at any point at any momentComprises the following steps:
εc(t0)＝ε0(t0)+ψ(t0)y (3-37)
σc(t0)＝E0(t0)[ε0(t0)+ψ(t0)y] (3-38)
t0the instantaneous stress of the steel bar at the moment is calculated according to the following formula:
σns(t0)＝Ens[ε0(t0)+ψ(t0)yns] (3-39)
in the formula, EnsIs the modulus of elasticity of the steel reinforcement.
For reference point 0, the constrained stress along the section constitutes the constrained internal force to the section, whose value can be respectively found by dividing the total pair of total cross-sectional areas, i.e. the cross-sectional area fraction, i.e.:
under the action of the limited internal force, corresponding deformation increment delta epsilon is generated until t moment0(t0,t),Δψ(t0T). To find this incremental deformation, it is considered equivalently that the section is subjected to a pair of opposite equivalent incremental external loads, Δ N and Δ M. Then, similar to equations (3-36), the strain increase Δ ε at time t at reference point 00(t0T) and the increment of curvature of the cross section Δ ψ (t)0T) may be expressed as follows:
in the formula (I), the compound is shown in the specification,
are respectively provided withThe area of the equivalent section adjusted by age, and the first-order moment and the second-order moment of the equivalent section to the horizontal axis passing through the 0 point are shown.
Thus, the strain and stress of the concrete in the cell at time t are:
εc(t0)＝εc(t0)+(Δε0(t0,t)+Δψ(t0,t)y) (3-43)
σc(t0,t)＝σc(t0)+Δσc(t0,t)+Δσc(t0,t) (3-45)
the stress of the steel bars in the unit at the moment t is as follows:
σns(t0,t)＝σns(t0)+Ens(Δε0(t0,t)+Δψ(t0,t)yns) (3-46)
the reinforced concrete structure is analyzed from any initial time t0Initially, the stress profile due to the limited shrinkage of the concrete is obtained as t0The respective stresses of the concrete and the reinforcing bars, which go through the moments at to t, are taken into account in this analysis. When Δ t is large, it can be subdivided into smaller n segments Δ ti(i is 1,2, L, n), and the calculation results of each segment are accumulated to obtain the final solution. As long as Δ t is chosen to be appropriately small, a reasonably accurate calculated value can theoretically be obtained, and a theoretically accurate solution will be obtained when Δ t is subdivided into infinitely small values. Thus, integrating the above equation over time yields a theoretically accurate solution.
Thus, the theoretical exact solution for the strain and stress of the concrete in the cell at time t is:
σc(t0,t)＝σc(t0)+Δσ(t0,t)y) (3-49)
the theoretical exact solution of the stress of the steel bars in the unit at time t is:
this analytical model is scalable or universal, in that it is constrained by shrinkage stresses Δ ε (t)0And t) calculating by using a superposition principle, and calculating the multidimensional condition by superposing the shrinkage stress of other shafts on the single-shaft calculation result, namely the method is also suitable for the multi-surface drying condition. For example, considering drying in three directions of x, y and z, drying in each direction and shrinkage-limited stress Δ σ caused by self-dryingx(t0,t)、Δσy(t0,t)、Δσz(t0T) calculation is the same as the above-mentioned Δ σ (t)0T) derivation process; and the change rate of humidity of each item under the drying action
The derivation process of (2) and the foregoing
The derivation processes are consistent; the change rate of humidity of each item under the action of self-drying
Also with the foregoing
The test results of (1) correspond to each other.
The invention mainly aims at the change of humidityThe method is characterized in that theoretical research is carried out on the problem of the caused shrinkage stress field, stress generation after shrinkage generated at a certain point in concrete due to drying and self-drying is restrained is mainly analyzed, the development rule of the restrained stress under the combined action of creep effect is considered, the shrinkage stress field at any moment is given, on the basis, time course analysis is carried out on the stress-strain change condition caused by restrained shrinkage of the reinforced concrete structure, and concrete stress, calculation formulas of strain and stress expression of the reinforced concrete at any moment and any point on the section are deduced. The self-drying effect in the concrete is considered in the derivation calculation process, which is a further place than the previous theory, and truly reflects the change condition of the humidity field in the concrete. Of course, due to the limited theoretical level, there is currently no well established theoretical expression for the relative humidity changes caused by the self-drying effect. Therefore, the stress Δ σ (t) is limited in contraction0T) expression ofsh(t0The fraction of the term t) that is self-drying is determined experimentally, i.e.
The concrete sealing agent is obtained by a relative humidity test of the inner pores of the sealed concrete.
Example two
As shown in fig. 3, the present invention further provides an analysis system for a concrete humidity field and a shrinkage stress field, comprising: the processing module is used for acquiring relative humidity data, constructing a relative humidity equation based on the relative humidity data, solving the relative humidity equation to obtain relative humidity, and calculating the relative humidity to obtain shrinkage strain;
the solving module is used for obtaining elastic strain and creep strain, constructing a stress time course analysis formula based on the shrinkage strain, the elastic strain and the creep strain, and calculating through the stress time course analysis formula to obtain an analysis result of the concrete humidity field and the shrinkage stress field. The system and the method of the present invention correspond to each other, and are not described herein in detail.
The foregoing illustrates and describes the principles, general features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (10)
1. A method for analyzing a concrete humidity field and a shrinkage stress field is characterized by comprising the following steps:
acquiring relative humidity data, constructing a relative humidity equation based on the relative humidity data, solving the relative humidity equation to obtain relative humidity, and calculating the relative humidity to obtain shrinkage strain;
and acquiring elastic strain and creep strain, constructing a stress time-course analysis formula based on the shrinkage strain, the elastic strain and the creep strain, and calculating by using the stress time-course analysis formula to obtain analysis results of the concrete humidity field and the shrinkage stress field.
2. The method for analyzing the concrete humidity field and the shrinkage stress field according to claim 1, wherein:
the relative humidity data comprises evaporation diffusion drying relative humidity variable quantity and self-drying relative humidity variable quantity, wherein the evaporation diffusion drying relative humidity variable quantity is obtained through calculation of a diffusion law, and the self-drying relative humidity variable quantity is obtained through calculation of hydration degree.
3. The method for analyzing the concrete humidity field and the shrinkage stress field according to claim 1, wherein:
the process of solving the humidity equation includes:
constructing boundary conditions, wherein the boundary conditions are concrete surface humidity boundary conditions, absolute humidity boundary conditions and concrete boundary conditions exposed in air;
and solving the humidity equation by a finite element method based on the boundary condition to obtain the relative humidity.
4. The method for analyzing the concrete humidity field and the shrinkage stress field according to claim 1, wherein:
the process of calculating the relative humidity includes:
and calculating the relative humidity by constructing a relation between the shrinkage strain and the relative humidity to obtain the shrinkage strain, wherein the ratio of the shrinkage strain to the relative humidity is a shrinkage coefficient, and the shrinkage coefficient is obtained by calculating the final shrinkage strain.
5. The method for analyzing the concrete humidity field and the shrinkage stress field according to claim 1, wherein:
the process of constructing the stress time course analysis formula comprises the following steps:
solving shrinkage strain, elastic strain and creep strain to obtain a stress formula, integrating with section curvature based on the stress formula to construct a stress time course analysis formula,
the system comprises a base, a tension sensor, a sensor and a controller, wherein the elastic strain is obtained by calculation based on the Huke's law, the creep strain comprises basic creep strain and dry creep strain, the dry creep strain is obtained by calculation based on a dry creep calculation formula, and the basic creep strain is obtained by the calculation of the elastic strain correlation.
6. The analysis system for the concrete humidity field and shrinkage stress field analysis method according to any one of claims 1 to 5, comprising:
the processing module is used for acquiring relative humidity data, constructing a relative humidity equation based on the relative humidity data, solving the relative humidity equation to obtain relative humidity, and calculating the relative humidity to obtain shrinkage strain;
the solving module is used for obtaining elastic strain and creep strain, constructing a stress time course analysis formula based on the shrinkage strain, the elastic strain and the creep strain, and calculating through the stress time course analysis formula to obtain an analysis result of the concrete humidity field and the shrinkage stress field.
7. The system for analyzing the concrete humidity field and the shrinkage stress field according to claim 6, wherein:
in the processing module, the relative humidity data comprises evaporation diffusion drying relative humidity variable quantity and self-drying relative humidity variable quantity, wherein the evaporation diffusion drying relative humidity variable quantity is obtained through calculation of a diffusion law, and the self-drying relative humidity variable quantity is obtained through calculation of hydration degree.
8. The system for analyzing the concrete humidity field and the shrinkage stress field according to claim 6, wherein:
the processing module comprises:
the first processing unit is used for constructing boundary conditions, wherein the boundary conditions are concrete surface humidity boundary conditions, absolute humidity boundary conditions and concrete boundary conditions exposed to air;
and the second processing unit solves the humidity equation by a finite element method based on the boundary condition to obtain the relative humidity.
9. The system for analyzing the concrete humidity field and the shrinkage stress field according to claim 6, wherein:
the processing module further comprises:
the third processing unit calculates the relative humidity by constructing a relation between the shrinkage strain and the relative humidity to obtain the shrinkage strain, wherein the ratio of the shrinkage strain to the relative humidity is a shrinkage coefficient, and the shrinkage coefficient is obtained by calculating the final shrinkage strain.
10. The system for analyzing the concrete humidity field and the shrinkage stress field according to claim 6, wherein:
the solving module comprises:
the first solving unit is used for solving shrinkage strain, elastic strain and creep strain to obtain a stress formula;
the second solving unit is integrated with the section curvature based on a stress formula to construct a stress time course analysis formula;
the system comprises a base, a tension sensor, a sensor and a controller, wherein the elastic strain is obtained by calculation based on the Huke's law, the creep strain comprises basic creep strain and dry creep strain, the dry creep strain is obtained by calculation based on a dry creep calculation formula, and the basic creep strain is obtained by the calculation of the elastic strain correlation.
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| CN114741771A (en) * | 2022-05-16 | 2022-07-12 | 武汉大学 | Double-tube concrete column bearing capacity calculation method considering annular deformation coefficient |
| CN115615820A (en) * | 2022-08-11 | 2023-01-17 | 河海大学 | Construction method of early-age concrete relative humidity-tensile stress coupling model |
| CN117494255A (en) * | 2023-10-16 | 2024-02-02 | 中国铁建港航局集团有限公司 | Rapid prediction method for concrete shrinkage of steel-concrete composite beam bridge under complex constraint |
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| CN114741771A (en) * | 2022-05-16 | 2022-07-12 | 武汉大学 | Double-tube concrete column bearing capacity calculation method considering annular deformation coefficient |
| CN114741771B (en) * | 2022-05-16 | 2023-08-15 | 武汉大学 | Double-pipe concrete column bearing capacity calculation method considering circumferential deformation coefficient |
| CN115615820A (en) * | 2022-08-11 | 2023-01-17 | 河海大学 | Construction method of early-age concrete relative humidity-tensile stress coupling model |
| CN115615820B (en) * | 2022-08-11 | 2023-05-16 | 河海大学 | Construction method of early-age concrete relative humidity-tensile stress coupling model |
| CN117494255A (en) * | 2023-10-16 | 2024-02-02 | 中国铁建港航局集团有限公司 | Rapid prediction method for concrete shrinkage of steel-concrete composite beam bridge under complex constraint |
| CN117494255B (en) * | 2023-10-16 | 2024-06-04 | 中国铁建港航局集团有限公司 | Rapid prediction method for concrete shrinkage of steel-concrete composite beam bridge under complex constraint |
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