CN102323976A

CN102323976A - Calculation method of shrinkage, creep and prestress loss of concrete bridges

Info

Publication number: CN102323976A
Application number: CN201110172001A
Authority: CN
Inventors: 刘沐宇; 卢志芳; 高宗余
Original assignee: Wuhan University of Technology WUT
Current assignee: Wuhan University of Technology WUT
Priority date: 2011-06-24
Filing date: 2011-06-24
Publication date: 2012-01-18
Anticipated expiration: 2031-06-24
Also published as: CN102323976B

Abstract

The invention provides a shrinkage creep and prestress loss computation method of a concrete bridge. According to the invention, the shrinkage creep and prestress loss computation method of the concrete bridge, in which the time variation and the uncertainty are simultaneously considered, is obtained by analyzing the time variation of concrete through utilizing an age-adjusted effective modulus method (AEMM) and analyzing the uncertainty of the concrete through utilizing an accurate and rapidly-sampled Latin hypercube sampling (LHS) method; a prestress loss computation formula in which the time variation and the uncertainty of shrinkage creep and the interaction between the shrinkage creep and reinforcement stress relaxation are simultaneously considered is deduced according to a prestressed reinforcing steel and concrete stress balance equation and deformation coordination conditions and on the basis of the AEEM method and the LHS method; and a prestress loss computation method of the concrete bridge, in which the shrinkage creep and the stress relaxation are considered, is formed. In the structural internal force value field interval computed according to the shrinkage creep and prestress loss computation method disclosed by the invention, the unfavorable stress state of the bridge structure can be considered from multiple aspects in the designing process, so that the reliability of structure computation result is higher and the structure safety is better.

Description

Calculation method of shrinkage, creep and prestress loss of concrete bridges

技术领域 technical field

本发明涉及交通运输业桥涵工程领域，特别是涉及一种考虑时变性和不确定性的混凝土桥梁收缩徐变及预应力损失计算方法。The invention relates to the field of bridge and culvert engineering in the transportation industry, in particular to a calculation method for shrinkage, creep and prestress loss of concrete bridges considering time variation and uncertainty.

背景技术 Background technique

预应力混凝土桥梁以其跨越能力强、施工技术成熟、行车舒适、工程造价低、养护简单等独特的优势，在桥梁工程领域具有广阔的工程应用前景。据不完全统计，在世界范围内已建桥梁中，混凝土桥梁在所有桥型中所占的比例最大：其中欧洲和美国的混凝土桥梁占所建桥梁的70％以上；我国比例更大，混凝土桥梁占90％以上。随着混凝土桥梁设计、施工技术的不断成熟，高性能高强混凝土材料的不断进步，混凝土桥梁由简支结构、小跨径连续结构、逐渐发展到大跨连续结构，而且不同桥型的跨径也在不断刷新。Prestressed concrete bridges have broad engineering application prospects in the field of bridge engineering due to their unique advantages such as strong spanning ability, mature construction technology, comfortable driving, low construction cost and simple maintenance. According to incomplete statistics, among the bridges built in the world, concrete bridges account for the largest proportion of all bridge types: among them, concrete bridges in Europe and the United States account for more than 70% of the bridges built; Accounted for more than 90%. With the continuous maturity of concrete bridge design and construction technology, and the continuous improvement of high-performance and high-strength concrete materials, concrete bridges have gradually developed from simply supported structures, small-span continuous structures, and large-span continuous structures, and the spans of different bridge types are also different. is constantly being refreshed.

在预应力混凝土桥梁飞速发展的同时，其建成的大跨径桥梁结构也逐渐出现了不同程度的病害。大跨径预应力混凝土连续梁桥主要采用箱形结构形式，运营数年后，70％以上的大跨径连续箱梁桥都出现了不同程度的病害，其中主梁跨中下挠与箱梁1/4L左右腹板开裂尤为突出，成为制约大跨径混凝土桥梁进一步发展的关键技术难题。如，1994年建成的广东南海金沙大桥为大跨径预应力混凝土连续刚构桥，6年后跨中下挠达22cm，箱梁腹板出现大量斜裂缝；1995年建成的黄石长江大桥为特大跨径预应力混凝土连续刚构桥，跨中下挠现已达70cm，箱梁也出现大量裂缝。许多连桥梁经过加固处理后，跨中下挠与箱梁腹板开裂仍不能得到很好控制，桥梁结构安全受到严重威胁，在社会上造成了不良影响，给国家带来了巨大经济损失。With the rapid development of prestressed concrete bridges, the built-up long-span bridge structures have gradually appeared various degrees of disease. Long-span prestressed concrete continuous girder bridges mainly adopt box-shaped structures. After several years of operation, more than 70% of long-span continuous box girder bridges have various degrees of damage. The web cracking around 1/4L is particularly prominent, which has become a key technical problem restricting the further development of long-span concrete bridges. For example, the Guangdong Nanhai Jinsha Bridge built in 1994 is a long-span prestressed concrete continuous rigid frame bridge. Six years later, the mid-span deflection reached 22 cm, and a large number of oblique cracks appeared in the web of the box girder; the Huangshi Yangtze River Bridge built in 1995 was an extra-large The mid-span deflection of the prestressed concrete continuous rigid frame bridge has reached 70cm, and a large number of cracks have appeared in the box girder. After many bridges have been reinforced, the mid-span deflection and the cracking of the box girder web cannot be well controlled. The safety of the bridge structure is seriously threatened, which has caused adverse effects on the society and brought huge economic losses to the country.

国内外学者分析这些病害问题后发现，导致箱梁结构出现跨中下挠与腹板开裂病害的主要原因有：①混凝土收缩徐变大。高强混凝土收缩徐变机理认识不充分，目前桥梁结构的各种收缩徐变计算方法，计算得到的跨中下挠值相差达30％以上，理论计算与桥梁实际受力状态存在明显差异。②大跨混凝土桥梁结构长期预应力损失大。混凝土收缩徐变和钢筋应力松弛引起的预应力损失在总损失中占到30％以上，是混凝土桥梁长期预应力损失的主要影响因素，决定桥梁结构的有效预应力，但目前相关的预应力损失计算方法计算结果差别较大，是影响桥梁结构跨中下挠与腹板开裂病害的主要因素之一。Scholars at home and abroad have analyzed these problems and found that the main reasons for the mid-span deflection and web cracking of the box girder structure are: ① Large shrinkage and creep of concrete. The shrinkage and creep mechanism of high-strength concrete is not fully understood. The various shrinkage and creep calculation methods of bridge structures currently have a difference of more than 30% in the mid-span deflection value, and there is a significant difference between theoretical calculation and the actual stress state of the bridge. ②The long-term prestress loss of long-span concrete bridge structure is large. The prestress loss caused by concrete shrinkage and creep and reinforcement stress relaxation accounts for more than 30% of the total loss. It is the main influencing factor of the long-term prestress loss of concrete bridges and determines the effective prestress of the bridge structure. However, the relevant prestress loss at present The calculation results of the calculation methods are quite different, which is one of the main factors affecting the mid-span deflection and web cracking of bridge structures.

针对以上问题，目前混凝土桥梁控制跨中下挠与腹板开裂病害的主要方法有：①增加梁体预拱度，改变预应力筋的布置方式。②上部结构部分采用钢箱梁或部分采用钢腹板提高腹板抗剪能力。③对既有跨中下挠与箱梁开裂的桥梁结构进行加固。这些技术在一定程度上减缓了跨中下挠与箱梁开裂病害，但这些技术均不是针对混凝土桥梁收缩徐变和预应力损失等主要病害原因而提出的解决方法，因而为能从根本上解决混凝土桥梁的病害问题，进一步完善和改进收缩徐变、预应力损失分析理论及计算方法是目前迫切需要解决的问题。In view of the above problems, the main methods for controlling the mid-span deflection and web cracking of concrete bridges are as follows: ① Increase the pre-camber of the beam body and change the arrangement of prestressed tendons. ② The superstructure part adopts steel box girder or part adopts steel web to improve the shear capacity of the web. ③Reinforce the existing bridge structure with mid-span deflection and box girder cracking. These technologies have slowed down the mid-span deflection and box girder cracking to a certain extent, but these technologies are not solutions to the main causes of concrete bridge shrinkage, creep and prestress loss, so they cannot be solved fundamentally. For the problems of concrete bridge diseases, it is an urgent problem to be solved at present to further perfect and improve the analysis theory and calculation method of shrinkage creep and prestress loss.

发明内容 Contents of the invention

本发明所要解决的技术问题是：提供一种混凝土桥梁收缩徐变及预应力损失计算方法，利用按龄期调整的有效模量法考虑其时变性，利用拉丁超立方抽样法考虑其不确定性，达到两种方法计算时同时考虑时变性和不确定性的目的。该方法在设计时能够多重考虑桥梁结构的不利受力状态，使结构计算结果保证率更高、结构安全性更好。The technical problem to be solved by the present invention is to provide a calculation method for concrete bridge shrinkage and creep and prestress loss, which uses the age-adjusted effective modulus method to consider its time-varying properties, and uses the Latin hypercube sampling method to consider its uncertainty , to achieve the purpose of considering both time-varying and uncertainties in the calculation of the two methods. This method can take multiple considerations of the unfavorable stress state of the bridge structure in the design, so that the guarantee rate of the structural calculation results is higher and the structural safety is better.

本发明所采用的技术方案是：混凝土桥梁收缩徐变及预应力损失计算方法，包括：The technical solution adopted in the present invention is: the calculation method of concrete bridge shrinkage and creep and prestress loss, including:

混凝土桥梁收缩徐变计算方法是根据拉丁超立方抽样随机有限元法得到不确定性参数的统计评估结果，根据统计评估结果得到混凝土收缩应变和徐变系数的集合区间，然后根据混凝土收缩徐变应力-应变关系、按龄期调整的有效模量函数、集合区间和叠加原理获得混凝土桥梁收缩徐变计算公式，形成一种考虑时变性和不确定性的混凝土桥梁收缩徐变分析方法，并在有限元分析软件中实现该收缩徐变计算方法。The calculation method of shrinkage and creep of concrete bridges is to obtain the statistical evaluation results of uncertainty parameters according to the Latin hypercube sampling stochastic finite element method. -Strain relationship, age-adjusted effective modulus function, set interval and superposition principle to obtain the calculation formula of concrete bridge shrinkage and creep, form a concrete bridge shrinkage and creep analysis method considering time-varying and uncertainties, and in a limited The shrinkage and creep calculation method is implemented in the meta-analysis software.

混凝土桥梁预应力损失计算方法是根据拉丁超立方抽样随机有限元法得到不确定性参数的统计评估结果，结合混凝土收缩徐变应力-应变关系、按龄期调整的有效模量函数和预应力筋应力-应变关系，得到混凝土收缩应变、徐变系数和钢筋应力松弛等综合作用引起的预应力损失集合区间，根据集合区间获得混凝土桥梁的预应力损失计算公式，形成考虑收缩徐变和应力松弛的混凝土桥梁预应力损失计算方法。The calculation method of prestress loss in concrete bridges is based on the statistical evaluation results of uncertain parameters obtained by the Latin hypercube sampling stochastic finite element method, combined with concrete shrinkage creep stress-strain relationship, age-adjusted effective modulus function and prestressed tendon According to the stress-strain relationship, the set range of prestress loss caused by the combined effects of concrete shrinkage strain, creep coefficient and steel bar stress relaxation is obtained, and the calculation formula of prestress loss of concrete bridges is obtained according to the set range, and the calculation formula considering shrinkage, creep and stress relaxation is formed. Calculation method of prestress loss in concrete bridges.

所述的计算方法，混凝土桥梁收缩徐变计算方法中，不确定性参数的统计评估结果、收缩应变和徐变系数的集合区间是按照下述方法得到的：In the calculation method described in the concrete bridge shrinkage and creep calculation method, the statistical evaluation results of the uncertainty parameters, the set interval of the shrinkage strain and the creep coefficient are obtained according to the following method:

A)引入不确定性参数

分别表示名义徐变系数、名义收缩系数的不确定性、混凝土立方体抗压强度f_cm、环境相对湿度RH和预应力荷载影响因素的作用；A) Introducing Uncertainty Parameters

Respectively represent the nominal creep coefficient, the uncertainty of the nominal shrinkage coefficient, the concrete cube compressive strength f _cm , the relative humidity of the environment RH and the influence factors of prestress load;

B)得到各不确定性参数基于标准值的置信界限为1-α的置信区间：B) Get each uncertainty parameter Confidence interval based on standard values with confidence bounds of 1-α:

式(1)中，α取值0.05，σ为标准差，n为样本数，z_α/2为正态分布置信界限值，

为

的置信区间下界，为的置信区间上界，i取值1、2…5；In formula (1), the value of α is 0.05, σ is the standard deviation, n is the number of samples, z _α/2 is the normal distribution confidence limit value,

for

The lower bound of the confidence interval of , for The upper bound of the confidence interval of , i takes the

value

1, 2...5;

C)根据不确定性参数

的置信区间，将区间进行n等分，得到n+1个边界点和n个子区间，然后根据式(1)对实际桥梁的各不确定性参数

进行取样；对名义徐变系数、名义收缩系数的不确定性参数

在每个子区间通过拉丁超立方抽样法随机抽取一个样本，然后对所有样本随机排列统计评估；C) According to the uncertainty parameter

The confidence interval of the interval is divided into n equal parts to obtain n+1 boundary points and n subintervals, and then the uncertainty parameters of the actual bridge are calculated according to formula (1)

Sampling; Uncertainty parameters for nominal creep coefficient and nominal shrinkage coefficient

Randomly draw a sample in each subinterval by Latin hypercube sampling method, and then randomly permutate all samples for statistical evaluation;

D)根据公路钢筋混凝土及预应力混凝土桥涵设计规范，结合步骤C的统计评估的结果，得到收缩应变和徐变系数集合区间：D) According to the highway reinforced concrete and prestressed concrete bridge and culvert design specifications, combined with the results of the statistical evaluation of step C, the shrinkage strain and creep coefficient set intervals are obtained:

式(2)中，ε_cs0为混凝土名义收缩系数，ε_cs(t，t_s)为收缩开始龄期为t_s、计算龄期为t的收缩应变，β_s(t-t_s)为收缩随时间发展的系数，β_RH为收缩与年平均湿度相关的系数，

为收缩与混凝土抗压强度相关的系数，并且：In formula (2), ε _cs0 is the nominal shrinkage coefficient of concrete, ε _cs (t, t _s ) is the shrinkage strain when the shrinkage start age is t _s and the calculation age is t, and β _s (tt _s ) is the shrinkage with time The coefficient of development, β _RH is the coefficient related to shrinkage and annual average humidity,

is the coefficient of shrinkage related to concrete compressive strength, and:

β_sc为依水泥种类而定的系数，φ₀为混凝土名义徐变系数，φ(t，t₀)为加载龄期为t₀、计算龄期为t的徐变系数，β_c(t-t₀)为加载后随时间发展的系数，φ_RH为徐变与年平均湿度相关的系数，

为徐变与混凝土抗压强度相关的系数，并且：β _sc is the coefficient depending on the type of cement, φ ₀ is the nominal creep coefficient of concrete, φ(t, t ₀ ) is the creep coefficient of loading age t ₀ and calculation age t, β _c (tt ₀ ) is the coefficient developed with time after loading, φ _RH is the coefficient related to creep and annual average humidity,

is the coefficient related to creep and concrete compressive strength, and:

β(t₀)为徐变随时间发展的函数，并且：β(t ₀ ) is a function of creep with time and:

$β β (({t t}_{00})) = = \frac{11}{00 . . 11 + + {t t}_{00}^{0.2 0.2}} - - - - - - ((22 c c))$

所述的计算方法，得到混凝土桥梁收缩徐变计算公式的方法为：Described calculation method, the method that obtains concrete bridge shrinkage and creep calculation formula is:

A)对加载龄期为t₀且应力连续变化的混凝土结构，任意时刻t的混凝土收缩徐变应力-应变关系表示为：A) For a concrete structure whose loading age is t ₀ and the stress changes continuously, the stress-strain relationship of concrete shrinkage and creep at any time t is expressed as:

${ϵ ϵ}_{c c} ((t t)) = = \frac{{σ σ}_{c c} (({t t}_{00}))}{E E. (({t t}_{00}))} [[11 + + φ φ ((t t,, {t t}_{00}))]] + + \frac{{σ σ}_{c c} ((t t)) - - {σ σ}_{c c} (({t t}_{00}))}{E E. ((t t,, {t t}_{00}))} + + {ϵ ϵ}_{cs cs} ((t t,, {t t}_{s the s})) - - - - - - ((33))$

式(2)中，ε_c(t)为任意时刻t时混凝土的应变值，σ_c(t0)、σ_c(t)分别为t₀、t时的混凝土应力，E(t₀)为混凝土在t₀时刻的弹性模量，E(t，t₀)为混凝土按龄期调整的有效模量，即加载龄期为t₀、计算龄期为t时的混凝土弹性模量；In formula (2), ε _c (t) is the strain value of concrete at any time t, σ _c (t0) and σ _c (t) are the concrete stresses at t ₀ and t, respectively, and E(t ₀ ) is the concrete The elastic modulus at time t ₀ , E(t, t ₀ ) is the effective modulus of concrete adjusted according to age, that is, the elastic modulus of concrete when the loading age is t ₀ and the calculated age is t;

B)按龄期调整的有效模量函数E(t，t₀)表示为：B) The age-adjusted effective modulus function E(t, t ₀ ) is expressed as:

$E E. ((t t,, {t t}_{00})) = = \frac{E E. (({t t}_{00}))}{11 + + χ χ ((t t,, {t t}_{00})) φ φ ((t t,, {t t}_{00}))} - - - - - - ((44))$

$χ χ ((t t,, {t t}_{00})) = = \frac{11}{11 - - R R ((t t,, {t t}_{00}))} - - \frac{11}{φ φ ((t t,, {t t}_{00}))} - - - - - - ((55))$

$R R ((t t,, {t t}_{00})) = = \frac{{σ σ}_{c c} ((t t))}{{σ σ}_{c c} (({t t}_{00}))} - - - - - - ((66))$

式中：χ(t，t₀)为混凝土的加载龄期为t₀、计算龄期为t时的老化系数，R(t，t₀)为混凝土加载龄期为t₀、计算龄期为t时的松弛系数；In the formula: χ(t, t ₀ ) is the aging coefficient when the loading age of concrete is t ₀ and the calculation age is t, R(t, t ₀ ) is the concrete loading age is t ₀ , and the calculation age is Relaxation coefficient at t;

C)根据(1)～(6)式，结合叠加原理得到任意时刻由混凝土桥梁收缩徐变产生的轴力N和弯矩M为：C) According to formulas (1)~(6), combined with the principle of superposition, the axial force N and bending moment M generated by the shrinkage and creep of the concrete bridge at any time can be obtained as:

$N N = = {Σ Σ}_{i i = = 11}^{n no} (({Σ Σ}_{j j = = 11}^{i i - - 11} η η (({t t}_{i i},, {t t}_{j j})) ΔN ΔN (({t t}_{j j})))) + + {Σ Σ}_{i i = = 11}^{n no} ((E E. (({t t}_{i i},, {t t}_{i i - - 11})) {A A}_{c c} {Δϵ Δϵ}_{cs cs} (({t t}_{i i},, {t t}_{i i - - 11})))) - - - - - - ((77))$

$M m = = {Σ Σ}_{i i = = 11}^{n no} (({Σ Σ}_{j j = = 11}^{i i - - 11} η η (({t t}_{i i},, {t t}_{j j})) ΔM ΔM (({t t}_{j j})))) + + {Σ Σ}_{i i = = 11}^{n no} ((E E. (({t t}_{i i},, {t t}_{i i - - 11})) {I I}_{c c} Δ Δ {ψ ψ}_{cs cs} (({t t}_{i i},, {t t}_{i i - - 11})))) - - - - - - ((88))$

$η η (({t t}_{i i},, {t t}_{i i - - 11})) = = \frac{E E. (({t t}_{i i},, {t t}_{i i - - 11}))}{E E. (({t t}_{j j}))} ((φ φ (({t t}_{i i},, {t t}_{j j})) - - φ φ (({t t}_{i i - - 11},, {t t}_{j j})))) - - - - - - ((99))$

式(7)～(9)中，Δε_cs(t_i，t_i-1)为t_i-1到t_i时刻的混凝土收缩应变增量，Δψ_cs(t_i，t_i-1)为t_i-1到t_i时刻的混凝土收缩引起的曲率增量，ΔN(t_j)、ΔM(t_j)分别为t_i到t_j时刻的轴力和弯矩增量，E(t_i，t_i-1)为t_i-1到t_i时刻的按龄期调整的有效模量，E(t_j)为t_j时刻混凝土的弹性模量，φ(t_i，t_j)为t_j到t_i时刻的混凝土徐变系数，I_c为混凝土截面的抗弯惯性矩，A_c为混凝土结构的截面面积，η(t_i，t_j)为中间参数。In formulas (7) to (9), Δε _cs (t _i , t _i-1 ) is the concrete shrinkage strain increment from time t _i-1 to t _i , and Δψ _cs (t _i , t _i-1 ) is t The curvature increment caused by concrete shrinkage from _i-1 to t _i , ΔN(t _j ) and ΔM(t _j ) are the axial force and bending moment increments from t _i to t _j respectively, E(t _i , t _i-1 ) is the age-adjusted effective modulus from t _i-1 to t _i , E(t _j ) is the elastic modulus of concrete at t _j time, φ(t _i , t _j ) is _the Concrete creep coefficient at time t _i , I _c is the moment of inertia of the concrete section, A _c is the cross-sectional area of the concrete structure, and η(t _i , t _j ) is an intermediate parameter.

所述的计算方法，运用APDL语言，使混凝土桥梁收缩徐变计算方法在有限元分析软件中得到实现：The calculation method uses the APDL language to realize the shrinkage and creep calculation method of the concrete bridge in the finite element analysis software:

在ANSYS程序计算前处理模块中，嵌入混凝土弹性模量随龄期调整的时随变化函数，即按龄期调整的有效模量进行时变性分析。在后处理模块中，利用APDL语言，编制PDS模块不确定性统计分析流程，赋予随机变量分布函数类型，运用拉丁超立方抽样法，通过随机变量参数统计分析参数置信区间对混凝土桥梁进行收缩徐变不确定性分析。具体流程见图1。In the pre-processing module of ANSYS program calculation, the age-adjusted time-varying function of the elastic modulus of concrete is embedded, that is, the age-adjusted effective modulus is used for time-varying analysis. In the post-processing module, use the APDL language to compile the uncertainty statistical analysis process of the PDS module, assign the random variable distribution function type, and use the Latin hypercube sampling method to analyze the shrinkage and creep of the concrete bridge through the random variable parameter statistical analysis parameter confidence interval Uncertainty Analysis. The specific process is shown in Figure 1.

所述的计算方法，混凝土桥梁预应力损失计算方法中，得到不确定性参数的统计评估结果，以及混凝土收缩应变、徐变系数和钢筋应力松弛等相互作用引起的预应力损失集合区间的方法为：Described calculation method, in the concrete bridge prestress loss calculation method, obtains the statistical evaluation result of uncertainty parameter, and the method for the prestress loss collection interval that the interaction such as concrete shrinkage strain, creep coefficient and steel bar stress relaxation causes is as follows: :

A)引入不确定性参数λ₁、λ₂、λ₃、λ₄、λ₅分别代表混凝土桥梁徐变系数、收缩应变的不确定性系数、混凝土28天立方体抗压强度f_cm、环境相对湿度RH和钢筋应力松弛的不确定性的影响；A) Introduce uncertainty parameters λ ₁ , λ ₂ , λ ₃ , λ ₄ , and λ ₅ to represent concrete bridge creep coefficient, uncertainty coefficient of shrinkage strain, concrete 28-day cubic compressive strength f _cm , and ambient relative humidity Influence of uncertainty in RH and reinforcement stress relaxation;

B)得到各不确定性参数λ_i基于标准值的置信界限为1-α的置信区间：B) Obtain the confidence interval of each uncertainty parameter λ _i based on the standard value with a confidence limit of 1-α:

$(({\overset{&OverBar; &OverBar;}{λ λ}}_{i i} - - \frac{σ σ}{\sqrt{n no}} {z z}_{α α / / 22},, {\overset{&OverBar; &OverBar;}{λ λ}}_{i i} + + \frac{σ σ}{\sqrt{n no}} {z z}_{α α / / 22})) = = [[\underset{&OverBar; &OverBar;}{λ λ},, \overset{&OverBar; &OverBar;}{λ λ}]] - - - - - - ((1010))$

式(10)中，α取值0.05，σ为标准差，n为样本数，z_α/2为正态分布置信界限值，λ为λ_i的置信区间下界，

为λ_i的置信区间上界，i取值1、2…5；In formula (10), the value of α is 0.05, σ is the standard deviation, n is the number of samples, z _α/2 is the confidence limit value of normal distribution, λ is the lower bound of the confidence interval of λ _i ,

is the upper bound of the confidence interval of λ _i , and i takes the

value

1, 2...5;

C)根据不确定性参数λ_i的置信区间，将区间进行n等分，得到n+1个边界点和n个子区间，然后根据式(10)对实际桥梁的各不确定性参数λ_i进行取样；对徐变系数、收缩应变的不确定性参数λ₁、λ₂，在每个子区间通过拉丁超立方抽样法随机抽取一个样本，然后对所有样本随机排列统计评估；C) According to the confidence interval of the uncertainty parameter λ _i , the interval is divided into n equal parts to obtain n+1 boundary points and n sub-intervals, and then according to the formula (10) for each uncertainty parameter λ _i of the actual bridge Sampling: For the uncertainty parameters λ ₁ and λ ₂ of creep coefficient and shrinkage strain, a sample is randomly selected in each sub-interval by the Latin hypercube sampling method, and then all samples are randomly arranged for statistical evaluation;

D)根据式(3)、(4)得到任意时刻t时混凝土因收缩徐变引起的应力-应变关系：D) According to formulas (3) and (4), the stress-strain relationship caused by shrinkage and creep of concrete at any time t can be obtained:

${ϵ ϵ}_{c c} ((t t)) = = \frac{{σ σ}_{c c} (({t t}_{00}))}{E E. (({t t}_{00}))} [[11 + + φ φ ((t t,, {t t}_{00}))]] + + \frac{[[{σ σ}_{c c} ((t t)) - - {σ σ}_{c c} (({t t}_{00}))]] [[11 + + χ χ ((t t,, {t t}_{00})) φ φ ((t t,, {t t}_{00}))]]}{E E. (({t t}_{00}))} + + {ϵ ϵ}_{cs cs} ((t t,, {t t}_{00})) - - - - - - ((1111))$

E)考虑预应力筋的应力松弛损失，得到任意时刻预应力钢筋的应力-应变关系为：E) Considering the stress relaxation loss of prestressed tendons, the stress-strain relationship of prestressed tendons at any time is obtained as:

${ϵ ϵ}_{p p} ((t t)) = = \frac{{σ σ}_{p p} ((t t)) - - {\overset{&OverBar; &OverBar;}{σ σ}}_{p p} ((t t))}{{E E.}_{p p}} - - - - - - ((1212))$

${\overset{&OverBar; &OverBar;}{σ σ}}_{p p} ((t t)) = = {σ σ}_{p p} (({t t}_{00})) [[\frac{{σ σ}_{p p} (({t t}_{00}))}{{f f}_{pk pk}} - - 0.55 0.55]] \frac{log log ((t t - - {t t}_{00}))}{4545} - - - - - - ((1313))$

式(12)、(13)中，ε_p(t)为预应力钢筋的应变值，E_p为预应力钢筋的弹性模量，σ_p(t₀)、σ_p(t)分别为预应力钢筋在t₀、t时刻的应力值，

为钢筋应力松弛引起的预应力损失，f_pk为预应力钢筋强度标准值；In formulas (12) and (13), ε _p (t) is the strain value of the prestressed steel bar, E _p is the elastic modulus of the prestressed steel bar, σ _p (t ₀ ), σ _p (t) are the prestressed steel bars The stress value of the steel bar at time t ₀ and time t,

is the prestress loss caused by reinforcement stress relaxation, and f _pk is the standard value of prestressed reinforcement strength;

F)根据公路钢筋混凝土及预应力混凝土桥涵设计规范，结合步骤C的统计评估的结果，以及式(13)，得到收缩应变和徐变系数集合区间：F) According to the highway reinforced concrete and prestressed concrete bridge and culvert design code, combined with the results of statistical evaluation in step C, and formula (13), the shrinkage strain and creep coefficient set intervals are obtained:

$\{\begin{matrix} {ϵ ϵ}_{cs cs} ((t t,, {t t}_{s the s})) = = {λ λ}_{22} {ϵ ϵ}_{cs cs 00} \cdot \cdot {β β}_{s the s} ((t t - - {t t}_{s the s})) \\ {ϵ ϵ}_{cs cs 00} = = {ϵ ϵ}_{s the s} (({λ λ}_{33} {f f}_{cm cm})) \cdot &Center Dot; {λ λ}_{44} {β β}_{RH RH} \\ φ φ ((t t,, {t t}_{00})) = = {λ λ}_{11} {φ φ}_{00} \cdot &Center Dot; {β β}_{c c} ((t t - - {t t}_{00})) \\ {φ φ}_{00} = = {λ λ}_{44} {φ φ}_{RH RH} \cdot \cdot β β (({λ λ}_{33} {f f}_{cm cm})) \cdot &Center Dot; β β (({t t}_{00})) \\ {\overset{&OverBar; &OverBar;}{σ σ}}_{p p} ((t t)) = = {λ λ}_{55} {σ σ}_{p p} (({t t}_{00})) [[\frac{{σ σ}_{p p} (({t t}_{00}))}{{f f}_{pk pk}} - - 0.55 0.55]] \frac{lg lg ((t t - - {t t}_{00}))}{4545} \end{matrix} {λ λ}_{i i} &Element; &Element; [[\underset{&OverBar; &OverBar;}{λ λ},, \overset{&OverBar; &OverBar;}{λ λ}]] - - - - - - ((1414))$

所述的计算方法，得到预应力损失计算公式的方法为：Described calculation method, the method that obtains prestress loss calculation formula is:

A)混凝土应力平衡方程为：A) Concrete stress balance equation is:

σ_c(t)＝-μρσ_p(t) (15)σ _c (t) = -μρσ _p (t) (15)

ρ＝1+e_op ²/r_c ² (16)ρ＝1+e _op ² /r _c ² (16)

r_c ²＝I_c/A_c (17)r _c ² =I _c /A _c (17)

μ＝A_p/A_c (18)μ=A _p /A _c (18)

式(15)～(18)中，σ_c(t)、σ_p(t)分别为混凝土和预应力钢筋在t时刻的应力变化值，A_p、A_c分别为预应力筋和混凝土截面面积，e_op为预应力钢筋重心到混凝土截面重心的距离，I_c为混凝土截面惯性矩；In formulas (15) to (18), σ _c (t) and σ _p (t) are the stress change values of concrete and prestressed reinforcement at time t, respectively, and A _p and A _c are the cross-sectional areas of prestressed reinforcement and concrete, respectively , e _op is the distance from the center of gravity of the prestressed steel bar to the center of gravity of the concrete section, and I _c is the moment of inertia of the concrete section;

B)在预应力筋同一水平高度，根据预应力钢筋和混凝土变形协同条件可得：B) At the same horizontal height of the prestressed reinforcement, according to the synergy condition of prestressed reinforcement and concrete deformation:

ε_c(t)-ε_c(t₀)＝ε_p(t)-ε_p(t₀) (19)ε _c (t)-ε _c (t ₀ )=ε _p (t)-ε _p (t ₀ ) (19)

式(19)中，ε_c(t)为混凝土的应变值，ε_p(t)为预应力钢筋的应变值；In formula (19), ε _c (t) is the strain value of concrete, and ε _p (t) is the strain value of prestressed steel bars;

C)根据式(11)～(19)，得到考虑混凝土收缩徐变时变性与钢筋应力松弛相互影响的预应力损失σ_ps(t)的计算公式为：C) According to the formulas (11) to (19), the calculation formula of the prestress loss σ _ps (t) considering the time-varying property of concrete shrinkage and creep and the stress relaxation of steel bars is obtained as follows:

${σ σ}_{ps ps} ((t t)) = = \frac{{ϵ ϵ}_{cs cs} ((t t,, {t t}_{00})) + + \frac{{σ σ}_{c c} (({t t}_{00})) φ φ ((t t,, {t t}_{00}))}{E E. (({t t}_{00}))} + + \frac{{\overset{&OverBar; &OverBar;}{σ σ}}_{p p} ((t t))}{{E E.}_{p p}}}{\frac{11}{{E E.}_{p p}} + + \frac{μρ μρ}{E E. (({t t}_{00}))} [[11 + + χ χ ((t t,, {t t}_{00})) φ φ ((t t,, {t t}_{00}))]]} - - - - - - ((2020))$

本发明与现有技术相比具有以下主要优点：Compared with the prior art, the present invention has the following main advantages:

常规的收缩徐变和预应力损失计算方法，获得的桥梁结构长期内力为一个确定性值。而本发明提出的混凝土桥梁收缩徐变和预应力损失计算方法，同时考虑其时变性和不确定性，获得的桥梁结构长期内力为值域区间，与常规计算方法相比，值域区间在设计时能够多重考虑桥梁结构的不利受力状态，使结构计算结果保证率更高、结构安全性更好。The conventional shrinkage creep and prestress loss calculation method can obtain a deterministic value for the long-term internal force of the bridge structure. And the calculation method of concrete bridge shrinkage and creep and prestress loss that the present invention proposes, consider its time-varying property and uncertainty simultaneously, the long-term internal force of bridge structure that obtains is the range interval, compares with the conventional calculation method, the range interval is in the design The unfavorable force state of the bridge structure can be considered multiple times, so that the structural calculation results have a higher guarantee rate and the structural safety is better.

附图说明 Description of drawings

图1为考虑时变性和不确定性的收缩徐变分析流程。Figure 1 shows the shrinkage and creep analysis process considering time-varying and uncertainties.

图2为混凝土简支梁徐变试验模型，图中：1表示分配梁；2为徐变试验梁；3为应变测点；4为挠度测点。Figure 2 is the concrete simply supported beam creep test model, in the figure: 1 represents the distribution beam; 2 is the creep test beam; 3 is the strain measurement point; 4 is the deflection measurement point.

图3为混凝土梁收缩试验模型图，图中：5为千分表；6为收缩试验梁。Fig. 3 is a model diagram of a concrete beam shrinkage test, in which: 5 is a dial gauge; 6 is a shrinkage test beam.

图4为徐变系数变化曲线图。Figure 4 is a graph of the variation of the creep coefficient.

图5为收缩应变变化曲线图。Figure 5 is a graph showing the change in shrinkage strain.

图6为预应力损失模型图，图中：7为φ8钢筋；8为φ6钢筋；9为φs15.2钢筋；10为φ8钢筋。Figure 6 is the prestress loss model diagram, in which: 7 is φ8 steel bar; 8 is φ6 steel bar; 9 is φs15.2 steel bar; 10 is φ8 steel bar.

图7为试验梁预应力损失对比分析图。Figure 7 is a comparative analysis diagram of the prestress loss of the test beam.

具体实施方式 Detailed ways

混凝土收缩徐变同时具有时变性和不确定性，而目前相关的研究均只考虑其中一种特性等问题，本发明通过提出混凝土桥梁收缩徐变及预应力损失计算方法，同时其考虑时变性和不确定性，获得桥梁结构内力值域区间，以解决混凝土桥梁收缩徐变、预应力损失计算与结构实际工作状态不相符的技术难题。The shrinkage and creep of concrete has both time-varying and uncertainties, and the current related research only considers one of the characteristics and other issues. Uncertainty, to obtain the range of internal force of the bridge structure, to solve the technical problems of concrete bridge shrinkage and creep, prestress loss calculation and the actual working state of the structure do not match.

本发明利用按龄期调整的有效模量法(AEMM法)分析混凝土的时变性，运用准确、快速抽样的拉丁超立方抽样随机有限元法(LHS法)分析混凝土的不确定性，获得同时考虑时变性和不确定性的混凝土桥梁收缩徐变分析方法；根据预应力筋和混凝土应力平衡方程及变形协同条件，基于AEMM法和LHS法，推导同时考虑收缩徐变时变性和不确定性、及其与钢筋松弛相互作用的预应力损失计算公式，形成考虑收缩徐变和应力松弛的混凝土桥梁预应力损失计算方法。其具体步骤如下：The present invention utilizes the age-adjusted effective modulus method (AEMM method) to analyze the time-varying properties of concrete, uses the accurate and rapid sampling Latin hypercube sampling random finite element method (LHS method) to analyze the uncertainty of concrete, and obtains the simultaneous consideration Time-varying and uncertain shrinkage and creep analysis methods of concrete bridges; according to the prestressed tendons and concrete stress balance equations and deformation coordination conditions, based on the AEMM method and LHS method, deduce the time-varying and uncertain shrinkage and creep, and The calculation formula of prestress loss interacting with reinforcement relaxation forms a calculation method of prestress loss of concrete bridges considering shrinkage creep and stress relaxation. The specific steps are as follows:

(1)考虑时变性和不确定性的混凝土桥梁收缩徐变分析方法，包括以下三个步骤：(1) The shrinkage and creep analysis method of concrete bridges considering time-varying and uncertainties includes the following three steps:

①建立考虑时变性的按龄期调整的有效模量函数①Establish an age-adjusted effective modulus function considering time-varying

$E E. ((t t,, {t t}_{00})) = = \frac{E E. (({t t}_{00}))}{11 + + χ χ ((t t,, {t t}_{00})) φ φ ((t t,, {t t}_{00}))}$

式中，E(t，t₀)为混凝土按龄期调整的有效模量，即加载龄期为t₀、计算龄期为t时的混凝土弹性模量(MPa)；E(t₀)为混凝土在t₀时刻的弹性模量；φ(t，t₀)为加载龄期t₀、计算龄期为t时的混凝土徐变系数；χ(t，t₀)为混凝土的老化系数，

R(t，t₀)为混凝土加载龄期为t₀、计算龄期为t时的松弛系数，

In the formula, E(t, t ₀ ) is the age-adjusted effective modulus of concrete, that is, the concrete elastic modulus (MPa) when the loading age is t ₀ and the calculated age is t; E(t ₀ ) is The elastic modulus of concrete at time t ₀ ; φ(t, t ₀ ) is the concrete creep coefficient when the loading age t ₀ and the calculated age is t; χ(t, t ₀ ) is the aging coefficient of concrete,

R(t, t ₀ ) is the relaxation coefficient when the loading age of concrete is t ₀ and the calculation age is t,

②构建考虑不确定性的拉丁超立方抽样随机有限元置信区间② Constructing Latin Hypercube Sampling Stochastic Finite Element Confidence Interval Considering Uncertainty

考虑混凝土桥梁徐变、收缩的不确定性，分别引入不确定性参数

来分别表示名义徐变系数、名义收缩系数的不确定性、混凝土立方体抗压强度f_cm、环境相对湿度RH和预应力荷载等影响因素的作用。Considering the uncertainty of concrete bridge creep and shrinkage, the uncertainty parameters are introduced respectively

To represent the effects of the nominal creep coefficient, the uncertainty of the nominal shrinkage coefficient, the concrete cube compressive strength f _cm , the relative humidity of the environment RH and the prestress load.

每个不确定性参数基于标准值的一个置信界限为1-α的置信区间：Each uncertainty parameter is based on a confidence interval with a confidence bound of 1-α for the standard value:

令：make:

式中，σ为标准差；n为样本数；z_α/2为正态分布置信界限值。In the formula, σ is the standard deviation; n is the number of samples; z _α/2 is the normal distribution confidence limit.

根据不确定性参数

置信区间，将区间进行n等分，得到n+1个边界点和n个子区间，对收缩应变和徐变系数，在每个子区间通过拉丁超立方抽样法随机抽取一个样本，然后对所有样本随机排列统计评估。According to the uncertainty parameter

Confidence interval, divide the interval into n equal parts, get n+1 boundary points and n sub-intervals, for shrinkage strain and creep coefficient, randomly select a sample in each sub-interval by Latin hypercube sampling method, and then randomly select all samples Permutation statistics evaluation.

③建立考虑时变性和不确定性的混凝土桥梁收缩徐变分析方法③Establish an analysis method for shrinkage and creep of concrete bridges considering time-varying and uncertainties

根据上述按龄期调整的有效模量函数和统计评估结果，得到收缩应变和徐变系数集合区间为：According to the above age-adjusted effective modulus function and statistical evaluation results, the set range of shrinkage strain and creep coefficient is obtained as:

式中，ε_cs0为混凝土名义收缩系数；φ₀为混凝土名义徐变系数。In the formula, _εcs0 is the nominal shrinkage coefficient of concrete; _φ0 is the nominal creep coefficient of concrete.

根据叠加原理和上式计算的混凝土桥梁收缩徐变不确定性区间，用按龄期调整的有效模量替换混凝土弹性模量E(τ)，则任意时刻由混凝土桥梁收缩徐变产生的内力可表示为：According to the superposition principle and the uncertainty interval of concrete bridge shrinkage and creep calculated by the above formula, the effective modulus adjusted by age is used to replace the concrete elastic modulus E(τ), then the internal force generated by the concrete bridge shrinkage and creep at any time can be Expressed as:

$N N = = {Σ Σ}_{i i = = 11}^{n no} (({Σ Σ}_{j j = = 11}^{i i - - 11} η η (({t t}_{i i},, {t t}_{j j})) ΔN ΔN (({t t}_{j j})))) + + {Σ Σ}_{i i = = 11}^{n no} ((E E. (({t t}_{i i},, {t t}_{i i - - 11})) {A A}_{c c} {Δϵ Δϵ}_{cs cs} (({t t}_{i i},, {t t}_{i i - - 11}))))$

$M m = = {Σ Σ}_{i i = = 11}^{n no} (({Σ Σ}_{j j = = 11}^{i i - - 11} η η (({t t}_{i i},, {t t}_{j j})) ΔM ΔM (({t t}_{j j})))) + + {Σ Σ}_{i i = = 11}^{n no} ((E E. (({t t}_{i i},, {t t}_{i i - - 11})) {I I}_{c c} Δ Δ {ψ ψ}_{cs cs} (({t t}_{i i},, {t t}_{i i - - 11}))))$

$η η (({t t}_{i i},, {t t}_{i i - - 11})) = = \frac{E E. (({t t}_{i i},, {t t}_{i i - - 11}))}{E E. (({t t}_{j j}))} ((φ φ (({t t}_{i i},, {t t}_{j j})) - - φ φ (({t t}_{i i - - 11},, {t t}_{j j}))))$

式中，Δε_cs(t_i，t_i-1)为t_i-1到t_i时刻的混凝土收缩应变增量，Δψ_cs(t_i，t_i-1)为t_i-1到t_i时刻的混凝土收缩引起的曲率增量，ΔN(t_j)、ΔM(t_j)分别为t_i到t_j时刻的轴力和弯矩增量，E(t_i，t_i-1)为t_i-1到t_i时刻的按龄期调整的有效模量，E(t_j)为t_j时刻混凝土的弹性模量，φ(t_i，t_j)为t_j到t_i时刻的混凝土徐变系数，I_c为混凝土截面的抗弯惯性矩，A_c为混凝土结构的截面面积，η(t_i，t_j)为中间参数。In the formula, Δε _cs (t _i , t _i-1 ) is the concrete shrinkage strain increment from t _i-1 to t _i , and Δψ _cs (t _i , t _i-1 ) is the concrete shrinkage strain increment from t _i-1 to t _i The curvature increment caused by concrete shrinkage, ΔN(t _j ) and ΔM(t _j ) are the axial force and bending moment increments from t _i to t _j respectively, and E(t _i , t _i-1 ) is t _i Age-adjusted effective modulus from _-1 to time t _i , E(t _j ) is the elastic modulus of concrete at time t _j , φ(t _i , t _j ) is the creep of concrete from time t _j to t _i coefficient, I _c is the moment of inertia of the concrete section, A _c is the cross-sectional area of the concrete structure, and η(t _i , t _j ) is the intermediate parameter.

如果计算中不考虑混凝土收缩的影响，则去掉轴力N和弯矩M两式的后部分即可。If the influence of concrete shrinkage is not considered in the calculation, the rear part of the two equations of axial force N and bending moment M can be removed.

(2)考虑收缩徐变和应力松弛的混凝土桥梁预应力损失计算方法(2) Calculation method for prestress loss of concrete bridges considering shrinkage, creep and stress relaxation

混凝土桥梁收缩徐变、预应力钢筋应力松弛的不确定性，主要表现在徐变系数、收缩应变和钢筋应力松弛引起预应力损失的不确定性等方面。根据各影响参数，分别采用λ₁、λ₂代表混凝土桥梁徐变系数、收缩应变的不确定性系数，采用λ₃、λ₄、λ₅分别考虑混凝土抗压强度、环境相对湿度RH和钢筋应力松弛的不确定性影响。The uncertainty of shrinkage and creep of concrete bridges and stress relaxation of prestressed steel bars is mainly manifested in the uncertainty of creep coefficient, shrinkage strain and prestress loss caused by stress relaxation of steel bars. According to each influencing parameter, λ ₁ and λ ₂ are used to represent the concrete bridge creep coefficient and uncertainty coefficient of shrinkage strain respectively, and λ ₃ , λ ₄ and λ ₅ are used to consider concrete compressive strength, ambient relative humidity RH and steel stress respectively Uncertainty effects of slack.

各不确定性参数基于标准值的置信界限为1-α的置信区间为：The confidence interval of each uncertainty parameter based on the confidence limit of the standard value is 1-α:

$(({\overset{&OverBar; &OverBar;}{λ λ}}_{i i} - - \frac{σ σ}{\sqrt{n no}} {z z}_{α α / / 22},, {\overset{&OverBar; &OverBar;}{λ λ}}_{i i} + + \frac{σ σ}{\sqrt{n no}} {z z}_{α α / / 22})) = = [[\underset{&OverBar; &OverBar;}{λ λ},, \overset{&OverBar; &OverBar;}{λ λ}]]$

根据不确定性参数λ_i置信区间，将区间进行n等分，得到n+1个边界点和n个子区间，对收缩应变和徐变系数，在每个子区间通过拉丁超立方抽样法随机抽取一个样本，然后对所有样本随机排列统计评估。According to the confidence interval of the uncertainty parameter λ _i , the interval is divided into n equal parts, and n+1 boundary points and n subintervals are obtained. For shrinkage strain and creep coefficient, a random sample is selected in each subinterval by Latin hypercube sampling method samples, and then random permutation statistics were evaluated for all samples.

根据各不确定性参数的置信区间和公路钢筋混凝土及预应力混凝土桥涵设计规范，得到收缩应变、徐变系数、以及钢筋应力松弛引起的预应力损失等分析结果的集合区间：According to the confidence interval of each uncertainty parameter and the design specification of highway reinforced concrete and prestressed concrete bridges and culverts, the set interval of analysis results such as shrinkage strain, creep coefficient, and prestress loss caused by reinforcement stress relaxation is obtained:

$\{\begin{matrix} {ϵ ϵ}_{cs cs} ((t t,, {t t}_{s the s})) = = {λ λ}_{22} {ϵ ϵ}_{cs cs 00} \cdot \cdot {β β}_{s the s} ((t t - - {t t}_{s the s})) \\ {ϵ ϵ}_{cs cs 00} = = {ϵ ϵ}_{s the s} (({λ λ}_{33} {f f}_{cm cm})) \cdot \cdot {λ λ}_{44} {β β}_{RH RH} \\ φ φ ((t t,, {t t}_{00})) = = {λ λ}_{11} {φ φ}_{00} \cdot &Center Dot; {β β}_{c c} ((t t - - {t t}_{00})) \\ {φ φ}_{00} = = {λ λ}_{44} {φ φ}_{RH RH} \cdot &Center Dot; β β (({λ λ}_{33} {f f}_{cm cm})) \cdot &Center Dot; β β (({t t}_{00})) \\ {\overset{&OverBar; &OverBar;}{σ σ}}_{p p} ((t t)) = = {λ λ}_{55} {σ σ}_{p p} (({t t}_{00})) [[\frac{{σ σ}_{p p} (({t t}_{00}))}{{f f}_{pk pk}} - - 0.55 0.55]] \frac{lg lg ((t t - - {t t}_{00}))}{4545} \end{matrix} {λ λ}_{i i} &Element; &Element; [[\underset{&OverBar; &OverBar;}{λ λ},, \overset{&OverBar; &OverBar;}{λ λ}]]$

考虑混凝土收缩徐变时变性和钢筋应力松弛相互影响的预应力损失计算公式为：The formula for calculating the prestress loss considering the time-variation of concrete shrinkage and creep and the stress relaxation of steel bars is as follows:

${σ σ}_{ps ps} ((t t)) = = \frac{{ϵ ϵ}_{cs cs} ((t t,, {t t}_{00})) + + \frac{{σ σ}_{c c} (({t t}_{00})) φ φ ((t t,, {t t}_{00}))}{E E. (({t t}_{00}))} + + \frac{{\overset{&OverBar; &OverBar;}{σ σ}}_{p p} ((t t))}{{E E.}_{p p}}}{\frac{11}{{E E.}_{p p}} + + \frac{μρ μρ}{E E. (({t t}_{00}))} [[11 + + χ χ ((t t,, {t t}_{00})) φ φ ((t t,, {t t}_{00}))]]}$

下面结合附图和实例对本发明做进一步详细说明。The present invention will be described in further detail below in conjunction with accompanying drawings and examples.

实施例1，考虑时变性和不确定性的混凝土桥梁收缩徐变分析方法：Example 1, the shrinkage and creep analysis method of concrete bridges considering time-varying and uncertainties:

(1)建立考虑时变性的按龄期调整的有效模量函数(1) Establish an age-adjusted effective modulus function considering time-varying

对加载龄期为t₀且应力连续变化的混凝土结构，其混凝土收缩徐变应力-应变关系可表示为：For a concrete structure whose loading age is t ₀ and the stress changes continuously, the stress-strain relationship of concrete shrinkage and creep can be expressed as:

${ϵ ϵ}_{c c} ((t t)) = = {σ σ}_{c c} (({t t}_{00})) [[\frac{11}{E E. (({t t}_{00}))} + + C C ((t t,, {t t}_{00}))]] + + {&Integral; &Integral;}_{{t t}_{00}}^{t t} [[\frac{11}{E E. ((τ τ))} + + C C ((t t,, τ τ))]] dσ dσ ((τ τ)) + + {ϵ ϵ}_{cs cs} ((t t,, {t t}_{s the s}))$

式中，t₀、τ、t分别表示加载龄期、加载后的某一龄期以及计算徐变时的混凝土龄期(d)；E(t₀)、E(τ)为混凝土在t₀、τ时刻的弹性模量(MPa)；σ_c(t₀)为在加载时刻t₀时混凝土的初应力(MPa)；C(t，τ)为混凝土徐变度；ε_cs(t，t_s)为收缩开始龄期为t_s、计算龄期为t时的混凝土收缩应变值。In the formula, t ₀ , τ, and t represent the loading age, a certain age after loading, and the concrete age (d) when calculating creep, respectively; E(t ₀ ), E(τ) are _concrete , modulus of elasticity (MPa) at time τ; σ _c (t ₀ ) is the initial stress of concrete (MPa) at loading time t ₀ ; C(t, τ) is concrete creep; ε _cs (t, t _s ) is the shrinkage strain value of concrete when the shrinkage start age is t _s and the calculated age is t.

而徐变度与徐变系数的关系为：The relationship between creep degree and creep coefficient is:

$C C ((t t,, {t t}_{00})) = = \frac{φ φ ((t t,, {t t}_{00}))}{E E. (({t t}_{00}))}$

式中，φ(t，t₀)为加载龄期t₀、计算龄期为t时的混凝土徐变系数。In the formula, φ(t, t ₀ ) is the concrete creep coefficient when the loading age t ₀ and the calculation age are t.

对上式积分部分运用中值定理可得：Applying the mean value theorem to the integral part of the above formula, we can get:

${ϵ ϵ}_{c c} ((t t)) = = \frac{{σ σ}_{c c} (({t t}_{00}))}{E E. (({t t}_{00}))} [[11 + + φ φ ((t t,, {t t}_{00}))]] + + \frac{{σ σ}_{c c} ((t t)) - - {σ σ}_{c c} (({t t}_{00}))}{E E. ((t t,, {t t}_{00}))} + + {ϵ ϵ}_{cs cs} ((t t,, {t t}_{s the s}))$

式中，E(t，t₀)为混凝土按龄期调整的有效模量，即加载龄期为t₀、计算龄期为t时的混凝土弹性模量；σ_c(t)为t时刻的混凝土应力。In the formula, E(t, t ₀ ) is the age-adjusted effective modulus of concrete, that is, the elastic modulus of concrete when the loading age is t ₀ and the calculated age is t; σ _c (t) is the concrete stress.

按龄期调整的有效模量函数可表示为：The age-adjusted effective modulus function can be expressed as:

$E E. (({t t,, t t}_{00})) = = \frac{E E. (({t t}_{00}))}{11 + + χ χ ((t t,, {t t}_{00})) φ φ ((t t,, {t t}_{00}))}$

式中，χ(t，t₀)为混凝土的老化系数，

In the formula, χ(t, t ₀ ) is the aging coefficient of concrete,

(2)构建考虑不确定性的拉丁超立方抽样随机有限元置信区间混凝土桥梁徐变、收缩的不确定性，主要表现在其影响因素的不确定性方面，因此引入不确定性参数

分别表示名义徐变系数、名义收缩系数的不确定性、混凝土立方体抗压强度f_cm、环境相对湿度RH和预应力荷载等主要影响因素的作用。(2) Construct a Latin hypercube sampling stochastic finite element confidence interval considering uncertainty The uncertainty of concrete bridge creep and shrinkage is mainly manifested in the uncertainty of its influencing factors, so the uncertainty parameter is introduced

Respectively represent the effects of the main influencing factors such as the nominal creep coefficient, the uncertainty of the nominal shrinkage coefficient, the concrete cube compressive strength f _cm , the relative humidity of the environment RH and the prestress load.

假定各不确定性参数均符合正态分布且相互独立，取抽样数目N＝15，抽样后根据各不确定性随机变量的概率分布，求出对应的确定性分析参数值。Assuming that each uncertainty parameter conforms to the normal distribution and is independent of each other, the sampling number N=15 is taken, and the corresponding deterministic analysis parameter value is obtained according to the probability distribution of each uncertainty random variable after sampling.

则混凝土桥梁收缩徐变不确定性参数的随机变量向量为：Then the random variable vector of the shrinkage and creep uncertainty parameters of the concrete bridge is:

i＝1，2，Λ，5 i=1, 2, Λ, 5

由于

是相互独立的，且5个不确定性参数都服从正态分布函数特征，则：because

are independent of each other, and the five uncertainty parameters all obey the characteristics of normal distribution function, then:

式中，μ是遵从正态分布的随机变量的均值；

为μ的无偏估计值；σ²是随机变量的方差，σ为标准差，下列各式σ意义相同；n为样本数。In the formula, μ is the mean value of a random variable following a normal distribution;

is the unbiased estimated value of μ; σ ² is the variance of the random variable, σ is the standard deviation, and the following formulas σ have the same meaning; n is the number of samples.

且

and

式中，z_α/2为正态分布置信界限值。In the formula, z _α/2 is the normal distribution confidence limit value.

这样就得到每个不确定性参数标准正态分布α分位点，以及基于标准值μ的一个置信界限为1-α的置信区间：This results in the standard normal distribution α quantiles for each uncertainty parameter, and a confidence interval based on the standard value μ with a confidence limit of 1-α:

令：make:

根据标准差σ和抽样样本数n，得到z_α/2，代入每个不确定性参数的均值和标准差即可求得各种置信水平的不确定性参数置信区间。According to the standard deviation σ and the number of samples n, z _α/2 is obtained, and by substituting the mean value and standard deviation of each uncertainty parameter, the confidence interval of the uncertainty parameter with various confidence levels can be obtained.

根据不确定性参数置信区间，将区间进行n等分，得到n+1个边界点和n个子区间，对收缩应变和徐变系数，在每个子区间通过拉丁超立方抽样法随机抽取一个样本，然后对所有样本随机排列统计评估。According to the uncertainty parameter Confidence interval, divide the interval into n equal parts, get n+1 boundary points and n sub-intervals, for shrinkage strain and creep coefficient, randomly select a sample in each sub-interval by Latin hypercube sampling method, and then randomly select all samples Permutation statistics evaluation.

(3)建立考虑时变性和不确定性的混凝土桥梁收缩徐变分析方法(3) Establish a shrinkage and creep analysis method for concrete bridges considering time-varying and uncertainties

根据叠加原理，以及上式计算的混凝土桥梁收缩徐变不确定性区间，用按龄期调整的有效模量替换混凝土弹性模量E(τ)，则任意时刻由混凝土桥梁收缩徐变产生的内力为：According to the principle of superposition and the uncertainty interval of shrinkage and creep of concrete bridges calculated by the above formula, replace the concrete elastic modulus E(τ) with the age-adjusted effective modulus, then the internal force generated by the shrinkage and creep of concrete bridges at any time for:

式中：Δε_cs(t_i，t_i-1)为收缩应变增量；Δψ_cs(t_i，t_i-1)为收缩引起的曲率增量，ΔN(t_j)、ΔM(t_j)为t_i到t_j时刻的轴力和弯矩增量；E(t_i，t_i-1)为按龄期调整的有效模量；E(t_j)为t_j时刻混凝土的弹性模量。In the formula: Δε _cs (t _i , t _i-1 ) is the shrinkage strain increment; Δψ _cs (t _i , t _i-1 ) is the curvature increment caused by shrinkage, ΔN(t _j ), ΔM(t _j ) is the axial force and bending moment increment from time t _i to t _j ; E(t _i , t _i-1 ) is the age-adjusted effective modulus; E(t _j ) is the elastic modulus of concrete at time t _j .

实施例2，考虑时变性和不确定性的混凝土桥梁收缩徐变分析方法应用：Example 2, the application of the shrinkage and creep analysis method of concrete bridges considering time-varying and uncertainties:

为验证提出的考虑时变性和不确定性的混凝土桥梁收缩徐变分析方法的正确性，通过ANSYS软件编制了计算分析流程，见图1，并运用该方法对混凝土试验模型进行收缩徐变效应分析。In order to verify the correctness of the proposed shrinkage and creep analysis method of concrete bridges considering time-varying and uncertainties, the calculation and analysis process was compiled by ANSYS software, as shown in Figure 1, and this method was used to analyze the shrinkage and creep effects of the concrete test model .

该计算分析流程具体过程为：ANSYS软件包括前处理模块和后处理模块。在前处理模块中(PREP7)建立按龄期调整的有效模量函数，然后进入求解模块(SOLU)对该有效模量进行时变性分析，通过GET命令对计算结果进行提取。随之进入了后处理模块。利用APDL语言编制PDS(ANSYS Parametric Design Language)模块，通过不确定性变量、分布函数、LHS变量矩阵等分析参数置信区间，然后根据叠加方法进入循环，结合按龄期调整的有效模量函数与LHS随机有限元计算内力和位移，并通过循环文件(file.loop)和不确定性变量灵敏度分析返回到参数置信区间，继续进行循环过程直至求解结果得到。The specific process of the calculation and analysis process is as follows: ANSYS software includes a pre-processing module and a post-processing module. The age-adjusted effective modulus function was established in the preprocessing module (PREP7), and then entered into the solution module (SOLU) for time-varying analysis of the effective modulus, and the calculation results were extracted through the GET command. Then enter the post-processing module. Use the APDL language to compile the PDS (ANSYS Parametric Design Language) module, analyze the confidence interval of the parameters through the uncertainty variable, distribution function, LHS variable matrix, etc., and then enter the cycle according to the superposition method, combining the age-adjusted effective modulus function and LHS Stochastic finite element calculation of internal force and displacement, and return to parameter confidence interval through loop file (file.loop) and uncertainty variable sensitivity analysis, and continue the loop process until the solution result is obtained.

徐变试验模型：采用直线配筋、后张拉的预应力混凝土简支梁，梁长355cm，截面尺寸为40cm×40cm，如图2所示。试验梁上下缘均施加预压应力，预应力钢筋采用φ15.20钢铰线，纵向钢筋采用φ12螺纹钢，箍筋采用φ8圆钢，梁体采用C50混凝土。徐变试验模型采用直线配筋和满堂支架方法施工，梁体混凝土浇注完毕强度达到设计值的85％后进行预应力张拉。试验梁采用跨中两点加载方式，集中荷载加载位置分别为L/4和3L/4截面，荷载均为6.0kN。Creep test model: a prestressed concrete simply supported beam with linear reinforcement and post-tensioning, the beam length is 355cm, and the cross-sectional size is 40cm×40cm, as shown in Figure 2. The upper and lower edges of the test beam are prestressed, the prestressed steel bar is made of φ15.20 steel hinge wire, the longitudinal steel bar is made of φ12 threaded steel, the stirrup is made of φ8 round steel, and the beam body is made of C50 concrete. The creep test model is constructed by using linear reinforcement and full support method, and the beam body concrete is poured and the strength reaches 85% of the design value, and then the prestressed tension is carried out. The test beam adopts a two-point loading method in the middle of the span, and the concentrated load loading positions are L/4 and 3L/4 sections respectively, and the load is 6.0kN.

收缩试验模型：混凝土收缩试验试件截面尺寸为15cm×15cm，试件长250cm。混凝土收缩试件如图3所示。为更好地反映环境温、湿度情况，混凝土收缩试验试件一次性浇注完成，且均未进行其他处理。试件内部沿试件长方向埋设振弦式应变计测试应变。Shrinkage test model: The cross-sectional size of the concrete shrinkage test specimen is 15cm×15cm, and the length of the specimen is 250cm. The concrete shrinkage specimens are shown in Figure 3. In order to better reflect the environmental temperature and humidity conditions, the concrete shrinkage test specimens were poured at one time without any other treatment. A vibrating wire strain gauge is embedded inside the specimen along the length of the specimen to measure the strain.

徐变计算结果如图4所示，收缩计算结果如图5所示。计算结果表明，采用本发明混凝土桥梁收缩徐变分析方法，计算得到的徐变系数、收缩应变值与试验值变化趋势一致且吻合良好。其中徐变系数、收缩应变确定性计算值与试验值差别很小，徐变系数最大差值仅为0.06，收缩应变最大差值仅为52uε，且试验值均位于95％置信界限范围的中部。由此可见，考虑时变性和不确定性的混凝土桥梁收缩徐变分析方法，计算混凝土桥梁结构的收缩徐变效应时，计算结果合理、可靠。The creep calculation results are shown in Figure 4, and the shrinkage calculation results are shown in Figure 5. The calculation results show that, by using the shrinkage and creep analysis method of the concrete bridge of the present invention, the calculated creep coefficient and shrinkage strain value are consistent with the test values and agree well with each other. Among them, the creep coefficient and shrinkage strain deterministically calculated values are very different from the test values, the maximum difference of creep coefficient is only 0.06, and the maximum difference of shrinkage strain is only 52uε, and the test values are all in the middle of the 95% confidence limit range. It can be seen that the shrinkage and creep analysis method of concrete bridges considering time-varying and uncertainties is reasonable and reliable when calculating the shrinkage and creep effects of concrete bridge structures.

实施例3，考虑收缩徐变和应力松弛的混凝土桥梁预应力损失计算方法：Embodiment 3, the calculation method of prestress loss of concrete bridge considering shrinkage creep and stress relaxation:

(1)考虑时变性和钢筋应力松弛的预应力损失计算公式(1) Calculation formula of prestress loss considering time variation and stress relaxation of reinforcement

当混凝土加载龄期由t₀变化至t时，由于混凝土桥梁收缩徐变和钢筋应力松弛的时变性，任意截面上混凝土的压应力和预应力筋的拉应力均会随时间而减小，且变化值相等，满足截面内力平衡条件：When the concrete loading age changes from t ₀ to t, due to the time-varying properties of concrete bridge shrinkage and creep and reinforcement stress relaxation, the compressive stress of concrete and the tensile stress of prestressed tendons on any section will decrease with time, and The change values are equal, and the internal force balance condition of the section is satisfied:

σ_c(t)＝-μρσ_p(t)σ _c (t) = -μρσ _p (t)

ρ＝1+e_op ²/r_c ² ρ＝1+e _op ² /r _c ²

r_c ²＝I_c/A_c r _c ² =I _c /A _c

μ＝A_p/A_c μ＝A _p /A _c

式中，σ_c(t)、σ_p(t)为混凝土和预应力钢筋在t时刻的应力值；A_p、A_c分别为预应力筋和混凝土截面面积；e_op为预应力钢筋重心到混凝土截面重心的距离；I_c为混凝土截面惯性矩。In the formula, σ _c (t) and σ _p (t) are the stress values of concrete and prestressed reinforcement at time t; A _p and A _c are the cross-sectional areas of prestressed reinforcement and concrete respectively; e _op is the center of gravity of prestressed reinforcement to The distance from the center of gravity of the concrete section; _Ic is the moment of inertia of the concrete section.

在预应力筋同一水平高度，根据预应力筋和混凝土变形协同条件可得：At the same horizontal height of prestressed tendons, according to the synergy condition of prestressed tendons and concrete deformation, it can be obtained:

ε_c(t)-ε_c(t₀)＝ε_p(t)-ε_p(t₀)ε _c (t)-ε _c (t ₀ )＝ε _p (t)-ε _p (t ₀ )

式中，ε_c(t)、ε_c(t₀)为混凝土在t和t₀时刻的应变值；ε_p(t)、ε_p(t₀)预应力钢筋在t和t₀时刻的应变值。In the formula, ε _c (t), ε _c (t ₀ ) are the strain values of concrete at time t and t ₀ ; ε _p (t), ε _p (t ₀ ) are the strain values of prestressed steel bars at time t and _t value.

对加载龄期为t₀且应力连续变化的混凝土桥梁，通过按龄期调整的有效模量法，来考虑混凝土结构收缩徐变的时变性时，任意时刻t混凝土的应力-应变关系：For a concrete bridge whose loading age is t ₀ and the stress changes continuously, when the age-adjusted effective modulus method is used to consider the time-varying nature of shrinkage and creep of the concrete structure, the stress-strain relationship of concrete at any time t is:

${ϵ ϵ}_{c c} ((t t)) = = \frac{{σ σ}_{c c} (({t t}_{00}))}{E E. (({t t}_{00}))} [[11 + + φ φ ((t t,, {t t}_{00}))]] + + \frac{[[{σ σ}_{c c} ((t t)) - - {σ σ}_{c c} (({t t}_{00}))]] [[11 + + χ χ ((t t,, {t t}_{00})) φ φ ((t t,, {t t}_{00}))]]}{E E. (({t t}_{00}))} + + {ϵ ϵ}_{cs cs} ((t t,, {t t}_{00}))$

式中，χ(t，t₀)为混凝土老化系数。简化计算时，χ(t，t₀)的取值范围一般为0.5～1.0。In the formula, χ(t, t ₀ ) is the concrete aging coefficient. When simplifying the calculation, the value range of χ(t, t ₀ ) is generally 0.5-1.0.

考虑预应力筋的应力松弛损失，得到任意时刻预应力钢筋的应力-应变关系为：Considering the stress relaxation loss of prestressed tendons, the stress-strain relationship of prestressed tendons at any time is obtained as:

${ϵ ϵ}_{p p} ((t t)) = = \frac{{σ σ}_{p p} ((t t)) - - {\overset{&OverBar; &OverBar;}{σ σ}}_{p p} ((t t))}{{E E.}_{p p}}$

${\overset{&OverBar; &OverBar;}{σ σ}}_{p p} ((t t)) = = {σ σ}_{p p} (({t t}_{00})) [[\frac{{σ σ}_{p p} (({t t}_{00}))}{{f f}_{pk pk}} - - 0.55 0.55]] \frac{lg lg ((t t - - {t t}_{00}))}{4545}$

式中，

为钢筋应力松弛引起的预应力损失；f_pk为预应力钢筋强度标准值。In the formula,

is the prestress loss caused by reinforcement stress relaxation; f _pk is the standard value of prestressed reinforcement strength.

根据上述公式整理得到，考虑混凝土收缩徐变时变性与钢筋应力松弛相互影响的预应力损失计算公式为：According to the above formulas, the formula for calculating the prestress loss considering the interaction between the time-varying property of concrete shrinkage and creep and the stress relaxation of steel bars is as follows:

(2)考虑时变性、不确定性及其钢筋应力松弛相互影响的预应力损失计算方法(2) Calculation method of prestress loss considering the interaction of time-varying, uncertainty and stress relaxation of reinforcement

则不确定性参数基于标准值的置信界限为1-α的置信区间为：Then the confidence interval of the uncertainty parameter based on the confidence limit of the standard value is 1-α:

根据不确定性参数λ_i置信区间，将区间进行n等分，得到n+1个边界点和n个子区间，对收缩应变和徐变系数，在每个子区间通过拉丁超立方抽样法随机抽取一个样本，然后对所有样本随机排列统计评估。According to the confidence interval of the uncertainty parameter λ _i , the interval is divided into n equal parts, and n+1 boundary points and n subintervals are obtained. For shrinkage strain and creep coefficient, a random sample is selected in each subinterval by Latin hypercube sampling samples, and then random permutation statistics were evaluated for all samples.

根据各不确定性参数的置信区间和公路钢筋混凝土及预应力混凝土桥涵设计规范，求解得到收缩应变、徐变系数、及钢筋应力松弛引起的预应力损失等的集合区间：According to the confidence interval of each uncertainty parameter and the design specification of highway reinforced concrete and prestressed concrete bridges and culverts, the collection interval of shrinkage strain, creep coefficient, and prestress loss caused by reinforcement stress relaxation is obtained:

$\{\begin{matrix} {ϵ ϵ}_{cs cs} ((t t,, {t t}_{s the s})) = = {λ λ}_{22} {ϵ ϵ}_{cs cs 00} \cdot \cdot {β β}_{s the s} ((t t - - {t t}_{s the s})) \\ {ϵ ϵ}_{cs cs 00} = = {ϵ ϵ}_{s the s} (({λ λ}_{33} {f f}_{cm cm})) \cdot &Center Dot; {λ λ}_{44} {β β}_{RH RH} \\ φ φ ((t t,, {t t}_{00})) = = {λ λ}_{11} {φ φ}_{00} \cdot \cdot {β β}_{c c} ((t t - - {t t}_{00})) \\ {φ φ}_{00} = = {λ λ}_{44} {φ φ}_{RH RH} \cdot \cdot β β (({λ λ}_{33} {f f}_{cm cm})) \cdot \cdot β β (({t t}_{00})) \\ {\overset{&OverBar; &OverBar;}{σ σ}}_{p p} ((t t)) = = {λ λ}_{55} {σ σ}_{p p} (({t t}_{00})) [[\frac{{σ σ}_{p p} (({t t}_{00}))}{{f f}_{pk pk}} - - 0.55 0.55]] \frac{lg lg ((t t - - {t t}_{00}))}{4545} \end{matrix} {λ λ}_{i i} &Element; &Element; [[\underset{&OverBar; &OverBar;}{λ λ},, \overset{&OverBar; &OverBar;}{λ λ}]]$

根据上式获得收缩应变、徐变系数、钢筋应力松弛引起应力损失的值域，代入第(1)条中的预应力损失计算公式中，即可获得考虑混凝土收缩徐变时变性与不确定性、及其与钢筋应力松弛相互影响的预应力损失计算值。According to the above formula, the value range of shrinkage strain, creep coefficient, and stress loss caused by reinforcement stress relaxation can be obtained, and then substituted into the calculation formula of prestress loss in item (1), the time-varying and uncertainties of concrete shrinkage and creep can be obtained , and the calculated value of the prestress loss that interacts with the stress relaxation of the steel bar.

实施例4，考虑收缩徐变和应力松弛的混凝土桥梁预应力损失计算方法的应用：Embodiment 4, the application of the calculation method of prestress loss of concrete bridge considering shrinkage creep and stress relaxation:

为验证提出的预应力损失计算方法的正确性，运用该方法对普通混凝土试验模型进行长期预应力损失值计算。In order to verify the correctness of the proposed calculation method of prestress loss, this method is used to calculate the long-term prestress loss value of the ordinary concrete test model.

试验模型：预应力损失试验模型为1片普通混凝土预应力试验简支梁，试验模型为100×200mm，采用φ^s15.2预应力钢绞线，后张法施工。其预应力损失采用钢弦式压力传感器测试，混凝土应变采用千分表监测。测试时间为第1个月每天测量1次，第2个月起每星期测量2次，半年后每星期测量1次，试验持续1年以上。试验模型如图6所示。Test model: The prestress loss test model is a simply supported beam of ordinary concrete prestress test, the test model is 100×200mm, and the φ ^s 15.2 prestressed steel strand is used for post-tensioning construction. The loss of prestress is tested with a steel string pressure sensor, and the strain of the concrete is monitored with a dial gauge. The test time is once a day in the first month, twice a week from the second month, and once a week after half a year, and the test lasts for more than one year. The test model is shown in Figure 6.

预应力损失计算结果如图7所示，预应力损失试验监测数据与提出的预应力损失方法计算的确定性值吻合良好，采用该方法计算得到的长期预应力损失值域区间，在进行预应力混凝土结构设计时，保证预应力损失值域区间值均满足规范要求，使结构长期预应力损失预测具有更大的保证率，使结构长期受力性能更安全、可靠。The calculation results of prestress loss are shown in Fig. 7. The monitoring data of prestress loss test are in good agreement with the deterministic value calculated by the proposed prestress loss method. When designing concrete structures, it is guaranteed that the range and interval of prestress loss meet the requirements of the code, so that the prediction of long-term prestress loss of the structure has a greater guarantee rate, and the long-term mechanical performance of the structure is safer and more reliable.

Claims

1. concrete-bridge shrinkage and creep and loss of prestress computing method is characterized in that:

Concrete-bridge shrinkage and creep computing method are the statistical estimation results that obtain uncertain parameters according to Latin hypercube sampling stochastic finite element method; The set that obtains the concrete shrinkage strain and the coefficient of creeping according to the statistical estimation result is interval; Obtain concrete-bridge shrinkage and creep computing formula according to concrete shrinkage and creep strain-stress relation, the effective modulus function of pressing adjustment in the length of time, set interval and superposition principle then; Form a kind of consideration time variation and probabilistic concrete-bridge shrinkage and creep analytical approach, and in finite element analysis software, realize these shrinkage and creep computing method;

Concrete-bridge loss of prestress computing method are the statistical estimation results that obtain uncertain parameters according to Latin hypercube sampling stochastic finite element method; In conjunction with the concrete shrinkage and creep strain-stress relation, by effective modulus function and the stress of prestressed steel-strain stress relation adjusted the length of time; The loss of prestress set that obtain the concrete shrinkage strain, the lax combined action of creep coefficient and reinforcement stresses causes is interval; According to the interval loss of prestress computing formula that obtains concrete-bridge of set, form the concrete-bridge loss of prestress computing method of considering shrinkage and creep and stress relaxation.

2. computing method according to claim 1 is characterized in that, in the computing method of concrete-bridge shrinkage and creep, statistical estimation result, the contraction strain of uncertain parameters and the set interval of the coefficient of creeping obtain according to following method:

A) introduce uncertain parameters

The uncertainty, the concrete cube compressive strength f that represent nominal creep coefficient, nominal contraction coefficient respectively _Cm, envionmental humidity RH and prestress load influential factors;

B) obtaining each uncertain parameters

is the fiducial interval of 1-α based on the fiducial limit of standard value:

In the formula (1), α value 0.05, σ is a standard deviation, n is a sample number, z _α/2Be normal distribution fiducial limit value,

For The fiducial interval lower bound,

For

The fiducial interval upper bound, i value 1,2 ... 5;

C) according to the fiducial interval of uncertain parameters

; The n five equilibrium is carried out in the interval; Obtain n+1 frontier point and n sub-interval, according to formula (1) each uncertain parameters

of actual bridge is taken a sample then; The creep uncertain parameters

of coefficient, nominal contraction coefficient of name is randomly drawed a sample in each sub-range through the Latin hypercube sampling, then to all sample random alignment statistical estimations;

D) contain design specifications according to highway reinforced concrete and prestressed concrete bridge, the result of the statistical estimation of integrating step C obtains contraction strain and creeps the coefficient sets interval:

In the formula (2), ε _Cs0Be concrete name contraction coefficient, ε _Cs(t, t _s) be t for shrinking beginning length of time _s, to calculate the length of time be the contraction strain of t, β _s(t-t _s) for shrinking the coefficient of development in time, β _RHBe the contraction coefficient relevant with mean annual humidity,

Be the contraction coefficient relevant with concrete crushing strength, and:

β _ScFor according to the fixed coefficient of cement kind, φ ₀Be the concrete name coefficient of creeping, φ (t, t ₀) for load age be t ₀, to calculate the length of time be the coefficient of creeping of t, β _c(t-t ₀) be the coefficient that develops in time after loading, φ _RHBe the coefficient relevant of creeping with mean annual humidity,

Be the coefficient relevant of creeping with concrete crushing strength, and:

β (t ₀) be the function of development in time of creeping, and:

β (t_{0}) = \frac{1}{0.1 + {t_{0}}^{0.2}} - - - (2 c) .

3. computing method according to claim 2 is characterized in that, the method that obtains concrete-bridge shrinkage and creep computing formula is:

A) be t to load age ₀And stress continually varying xoncrete structure, the concrete shrinkage and creep strain-stress relation of any time t is expressed as:

ϵ_{c} (t) = \frac{σ_{c} (t_{0})}{E (t_{0})} [1 + φ (t, t_{0})] + \frac{σ_{c} (t) - σ_{c} (t_{0})}{E (t, t_{0})} + ϵ_{cs} (t, t_{s}) - - - (3)

In the formula (2), ε _cConcrete strain value when (t) being any time t, σ _c(t ₀), σ _c(t) be respectively t ₀, the concrete stress during t, E (t ₀) be that concrete is at t ₀Elastic modulus constantly, E (t, t ₀) be the effective modulus of concrete by adjustment in the length of time, promptly load age is t ₀, calculate the modulus of elasticity of concrete when being t the length of time;

B) the effective modulus function E (t, the t that adjust by the length of time ₀) be expressed as:

E (t, t_{0}) = \frac{E (t_{0})}{1 + χ (t, t_{0}) φ (t, t_{0})} - - - (4)

χ (t, t_{0}) = \frac{1}{1 - R (t, t_{0})} - \frac{1}{φ (t, t_{0})} - - - (5)

R (t, t_{0}) = \frac{σ_{c} (t)}{σ_{c} (t_{0})} - - - (6)

In the formula: χ (t, t ₀) be that concrete load age is t ₀, calculate the aging coefficient when being t the length of time, R (t, t ₀) for the concrete load age be t ₀, calculate the coefficient of relaxation when being t the length of time;

C), combine superposition principle to obtain any time to be by the axle power N and the moment M of concrete-bridge shrinkage and creep generation according to (1)～(6) formulas:

N = Σ_{i = 1}^{n} (Σ_{j = 1}^{i - 1} η (t_{i}, t_{j}) ΔN (t_{j})) + Σ_{i = 1}^{n} (E (t_{i}, t_{i - 1}) A_{c} {Δϵ}_{cs} (t_{i}, t_{i - 1})) - - - (7)

M = Σ_{i = 1}^{n} (Σ_{j = 1}^{i - 1} η (t_{i}, t_{j}) ΔM (t_{j})) + Σ_{i = 1}^{n} (E (t_{i}, t_{i - 1}) I_{c} Δ ψ_{cs} (t_{i}, t_{i - 1})) - - - (8)

η (t_{i}, t_{i - 1}) = \frac{E (t_{i}, t_{i - 1})}{E (t_{j})} (φ (t_{i}, t_{j}) - φ (t_{i - 1}, t_{j})) - - - (9)

In formula (7)～(9), Δ ε _Cs(t _i, t _I-1) be t _I-1To t _iConcrete shrinkage strain increment constantly, Δ ψ _Cs(t _i, t _I-1) be t _I-1To t _iThe curvature increment that concrete shrinkage constantly causes, Δ N (t _j), Δ M (t _j) be respectively t _iTo t _jAxle power and moment of flexure increment constantly, E (t _i, t _I-1) be t _I-1To t _iEffective modulus constantly by adjustment in the length of time, E (t _j) be t _jConcrete elastic modulus of the moment, φ (t _i, t _j) be t _jTo t _iConcrete creep coefficient constantly, I _cBe the bending resistance moment of inertia of concrete section, A _cBe the area of section of xoncrete structure, η (t _i, t _j) be intermediate parameters.

4. computing method according to claim 3; It is characterized in that: the computing method that realize this shrinkage and creep in the finite element analysis software are handled through the APDL language; Its treatment step comprises: with changing function, promptly the effective modulus by adjustment in the length of time is carried out the time variation analysis when at first the embedding modulus of elasticity of concrete was adjusted with the length of time in ANSYS program calculating pre-processing module; Calculate in the post-processing module in the ANSYS program then; Utilize APDL language establishment PDS module to realize uncertain statistical study flow process; Give stochastic variable distribution function type; Through stochastic variable parametric statistics methods analyst parametric confidence interval, concrete-bridge is carried out the shrinkage and creep uncertainty analysis.

5. computing method according to claim 1; It is characterized in that: in the concrete-bridge loss of prestress computing method; Obtain the statistical estimation result of uncertain parameters, and the interval method of loss of prestress set that concrete shrinkage strain, creep coefficient and the interaction of reinforcement stresses relaxation phase cause is:

A) introduce uncertain parameters λ ₁, λ ₂, λ ₃, λ ₄, λ ₅Represent creep 28 days cubic compressive strength f of coefficient of uncertainty, concrete of coefficient, contraction strain of concrete-bridge respectively _Cm, probabilistic influence that envionmental humidity RH and reinforcement stresses are lax;

B) obtain each uncertain parameters λ _iFiducial limit based on standard value is the fiducial interval of 1-α:

({\overset{&OverBar;}{λ}}_{i} - \frac{σ}{\sqrt{n}} z_{α / 2}, {\overset{&OverBar;}{λ}}_{i} + \frac{σ}{\sqrt{n}} z_{α / 2}) = [\underset{&OverBar;}{λ}, \overset{&OverBar;}{λ}] - - - (10)

In the formula (10), α value 0.05, σ is a standard deviation, n is a sample number, z _α/2Be normal distribution fiducial limit value, λBe λ _iThe fiducial interval lower bound,

Be λ _iThe fiducial interval upper bound, i value 1,2 ... 5;

C) according to uncertain parameters λ _iFiducial interval, the n five equilibrium is carried out in the interval, obtain n+1 frontier point and n sub-interval, then according to formula (10) each uncertain parameters λ to actual bridge _iTake a sample; Uncertain parameters λ to the coefficient of creeping, contraction strain ₁, λ ₂, randomly draw a sample in each sub-range through the Latin hypercube sampling, then to all sample random alignment statistical estimations;

D) according to formula (3), concrete caused because of shrinkage and creep when (4) obtained any time t strain-stress relation:

ϵ_{c} (t) = \frac{σ_{c} (t_{0})}{E (t_{0})} [1 + φ (t, t_{0})] + \frac{[σ_{c} (t) - σ_{c} (t_{0})] [1 + χ (t, t_{0}) φ (t, t_{0})]}{E (t_{0})} + ϵ_{cs} (t, t_{0}) - - - (11)

E) stress relaxation of considering presstressed reinforcing steel is lost, and the strain-stress relation that obtains any time deformed bar is:

ϵ_{p} (t) = \frac{σ_{p} (t) - {\overset{&OverBar;}{σ}}_{p} (t)}{E_{p}} - - - (12)

{\overset{&OverBar;}{σ}}_{p} (t) = σ_{p} (t_{0}) [\frac{σ_{p} (t_{0})}{f_{pk}} - 0.55] \frac{\log (t - t_{0})}{45} - - - (13)

In formula (12), (13), ε _p(t) be the strain value of deformed bar, E _pBe the elastic modulus of deformed bar, σ _p(t ₀), σ _p(t) be respectively deformed bar at t ₀, t stress value constantly,

Be the lax loss of prestress that causes of reinforcement stresses, f _PkBe the deformed bar strength standard value;

F) contain design specifications according to highway reinforced concrete and prestressed concrete bridge, the result of the statistical estimation of integrating step C, and formula (13) obtain contraction strain and creep the coefficient sets interval:

\{\begin{matrix} ϵ_{cs} (t, t_{s}) = λ_{2} ϵ_{cs 0} \cdot β_{s} (t - t_{s}) \\ ϵ_{cs 0} = ϵ_{s} (λ_{3} f_{cm}) \cdot λ_{4} β_{RH} \\ φ (t, t_{0}) = λ_{1} φ_{0} \cdot β_{c} (t - t_{0}) \\ φ_{0} = λ_{4} φ_{RH} \cdot β (λ_{3} f_{cm}) \cdot β (t_{0}) \\ {\overset{&OverBar;}{σ}}_{p} (t) = λ_{5} σ_{p} (t_{0}) [\frac{σ_{p} (t_{0})}{f_{pk}} - 0.55] \frac{\lg (t - t_{0})}{45} \end{matrix} λ_{i} &Element; [\underset{&OverBar;}{λ}, \overset{&OverBar;}{λ}] - - - (14) .

6. computing method according to claim 5 is characterized in that, the method that obtains the loss of prestress computing formula is:

A) the concrete stress balance equation is:

σ _c(t)＝-μρσ _p(t) (15)

ρ＝1+e _op ²/r _c ² (16)

r _c ²＝I _c/A _c (17)

μ＝A _p/A _c (18)

In formula (15)～(18), σ _c(t), σ _p(t) be respectively concrete and deformed bar at t STRESS VARIATION value constantly, A _p, A _cBe respectively presstressed reinforcing steel and concrete section area, e _OpBe the distance of deformed bar center of gravity to the concrete section center of gravity, I _cBe the concrete section moment of inertia;

B), can get according to deformed bar and concrete deformation cooperation condition in the same level height of presstressed reinforcing steel:

ε _c(t)-ε _c(t ₀)＝ε _p(t)-ε _p(t ₀) (19)

In the formula (19), ε _c(t) be concrete strain value, ε _p(t) be the strain value of deformed bar;

C), obtain considering concrete shrinkage and creep time variation and the reinforcement stresses interactional loss of prestress σ that relaxes according to formula (11)～(19) _Ps(t) computing formula is:

σ_{ps} (t) = \frac{ϵ_{cs} (t, t_{0}) + \frac{σ_{c} (t_{0}) φ (t, t_{0})}{E (t_{0})} + \frac{{\overset{&OverBar;}{σ}}_{p} (t)}{E_{p}}}{\frac{1}{E_{p}} + \frac{μρ}{E (t_{0})} [1 + χ (t, t_{0}) φ (t, t_{0})]} - - - (20) .