Identification of multiple open and fatigue cracks in beam-like structures using wavelets on deflection signals

A novel method for damage detection of multi-cracked beam-like structures by analyzing the static deflection is presented. The damage incurred produces a change in the stiffness of the beam. This causes a localized singularity which can be identified by a wavelet analysis of the displacement response. The existence and location of the cracks can be revealed by positions of the peaks in the continuous wavelet transform (CWT). To achieve this, the static profile of beams is analyzed with Gauss2 wavelet to identify the cracks. Beams under some ideal boundary and prescribed load conditions are considered. The deflected shape of the beam with open and fatigue cracks has been simulated under static loading using lumped crack models adopted from fracture mechanics and involving various degrees of complexity. The deflection of cracked beam in closed form for several cases of loads, crack sizes, and crack locations is calculated, and an explicit expression for the damage index (DI), based on CWT, is developed; it is demonstrated that the proposed damage index does not depend on mechanical properties of a homogeneous beam, and that the DI of one crack does not depend on the size and location of other cracks in a multiple cracked beam. Hence, the obtained expression for the DI can be used to find the size of each crack independently. Numerical results show that the method can detect cracks of small depth and is also applicable under the presence of measurement noise.     

爆炸荷载下基于细观建模的素/钢筋混凝土板破坏模式

为了获得爆炸荷载下细观结构对素/钢筋混凝土板的影响,采用随机骨料投放建立了素/钢筋混凝土板细观模型。利用LS-DYNA对基于细观建模的钢筋混凝土板进行爆炸荷载作用下的数值模拟,通过与实验以及均质建模方法进行比较,验证了细观建模方法的准确性。进而研究了基于细观建模的素/钢筋混凝土板在不同爆炸荷载下的结构响应,获得了素/钢筋混凝土板的响应过程和破坏模式。结果表明:在低药量（1、2 kg）爆炸荷载下,细观结构对素/钢筋混凝土板的影响较小,其破坏模式以纵横塑性铰线破坏为主,药量越大,铰线越多;在高药量（5、10和15 kg）爆炸荷载下,细观结构对素/钢筋混凝土板的影响较大,与均质模型相比存在较大差异,细观素/钢筋混凝土板以爆坑为中心,产生环向与径向裂纹,药量越大,圆坑越大,裂纹越多,板局部破坏越严重。     

NUMERICAL SIMULATION OF CRACK GROWTH OF REINFORCED CONCRETE FLEXURAL MEMBERS BASED ON XFEM1)

基于最大主应力准则,利用扩展有限元法对钢筋混凝土三点弯曲梁的裂纹扩展进行数值模拟。通过与已有模型试验结果的比对,验证了该方法的准确性与有效性。研究发现,带裂纹钢筋混凝土构件的裂纹扩展与力学性能不但受到单裂纹的尺寸、位置、倾角的影响,而且还受多裂纹间位置关系的影响;其中,裂纹横向分布位置和裂纹纵向分布位置是影响带裂纹钢筋混凝土梁裂缝扩展的主要因素。     

Multiple Crack Detection of Concrete Structures Using Impedance-based Structural Health Monitoring Techniques

This paper presents a feasibility study for practical applications of an impedance-based real-time health monitoring technique applying PZT (Lead–Zirconate–Titanate) patches to concrete structures. First, comparison between experimental and analytical studies for damage detection on a plain concrete beam is made. In the experimental study, progressive surface damage inflicted artificially on the plain concrete beam is assessed by using both lateral and thickness modes of the PZT patches. Then, an analytical study based on finite element (FE) models is carried out to verify the validity of the experimental result. Secondly, multiple (shear and flexural) cracks incurred in a reinforced concrete (RC) beam under a third point bending test are monitored continuously by using a sensor array system composed of the PZT patches. In this study, a root mean square deviation (RMSD) in the impedance signatures of the PZT patches is used as a damage indicator.     

钢筋混凝土开裂角软化薄膜模型

开裂角介于固定角和转动角之间,是裂缝实际的开展方向角.通过建立平衡方程、协调方程、钢筋和混凝土本构方程、泊松比效应系数方程,提出了钢筋混凝土开裂角软化薄膜模型,该模型考虑了拉应变与压应变的相互作用.本文还给出从应力到应变的计算方法,与传统从应变到应力的计算方法相比,该方法无须进行反复试算,计算简便.通过与8块钢筋混凝土薄板试验结果的比较,验证了所提出开裂角软化薄膜模型及其算法的正确性.     

A micromechanical analysis of damage propagation in fluid-saturated cracked mediaUne analyse micromécanique de la propagation de l'endommagement d'une fissure sous pression de fluide

We first revisit the well known framework of Linear Elastic Fracture Mechanics (LEFM) in the case of a fluid-saturated crack. We next consider a r.e.v. of cracked medium comprising a family of cracks characterized by the corresponding crack density parameter ε. Generalizing the classical energy approach of LEFM, the proposed damage criterion is written on the thermodynamic force associated with ε, which is estimated by means of standard homogenization schemes. This criterion proves to involve a macroscopic effective strain tensor, or alternatively the Terzaghi effective stress tensor. The stability of damage propagation is discussed for various homogenization schemes. A comparison with experimental results is presented in the case of a uniaxial tensile test on concrete. To cite this article: L. Dormieux et al., C. R. Mecanique 334 (2006).     

钢筋混凝土结构锈胀开裂宽度的试验研究及预测模型

设计了45片钢筋混凝土(RC)构件,基于RC构件通电加速锈蚀,对该批构件进行腐蚀试验研究,测试了锈胀裂缝宽度及其位置和发生时间。以钢筋锈蚀率、保护层锈胀开裂、锈胀裂缝宽度、相对保护层厚度和混凝土强度为分析参数,结合测试数据,利用加速腐蚀和自然腐蚀的对应关系,通过数理统计回归分析建立了锈胀开裂宽度的预测模型。分析了各参数对锈胀开裂扩展的影响。该模型对RC结构耐久性设计提供一定的参考。使用本文建立的模型以及规范模型对文献试验数据和一座服役近40年的实桥构件的锈蚀率和锈胀裂缝宽度进行了预测,计算结果表明本文模型有较强的适用性,能够用于实桥锈胀损伤分析。     

Formulation and numerical implementation of a constitutive law for concrete with strain-based damage and plasticity

A triaxial constitutive law for concrete within the framework of isotropic damage combined with plasticity is proposed in this paper. It covers typical characteristics of concrete like non-linear uniaxial compression and tension, bi- and triaxial failure criteria and dilatancy with a unified strain-based approach. Thus, this model is quite simple and especially suitable for strain-driven methods like common finite elements. It is complemented with a regularization method based on the crack band approach. A further issue is discussed with procedures for the model parameter determination for a wide range of concrete grades. The application of the model is demonstrated with typical benchmark tests for plain concrete.     

Modèle de comportement mécanique du béton armé corrodéMechanical model of reinforced concrete damaged by steel corrosion

This article deals with an analytical mechanical model of reinforced concrete damaged by steels corrosion. It is based on the taking into account of local bond between steel and the tensile concrete located between the cracks. Then, this model allows to quantify the coupled effect of steel cross section reduction and loss of bond strength due to steel corrosion on mechanical behaviour of reinforced concrete. To cite this article: A. Castel et al., C. R. Mecanique 330 (2002) 45–50     

JPC聚能装药对钢筋混凝土墙毁伤效应的试验与数值模拟研究

为了满足高侵深和大穿孔的要求,设计一种聚能杆式弹丸（jetting projectile charge, JPC）,开展大尺寸钢筋混凝土墙的毁伤效应试验。在此基础上,基于修正参数的K&C(Karagozian&Case)模型进行数值模拟,研究JPC高速侵彻和爆炸冲击波对钢筋混凝土墙的联合破坏作用,分析墙体厚度对破坏效果的影响规律。结果表明,在1.67倍和2.50倍装药直径的炸高条件下,JPC均能够有效贯穿80 cm(6.67倍装药直径)厚的钢筋混凝土墙,形成直径大于6 cm(0.50倍装药直径)的柱状孔洞;聚能装药的多载荷毁伤特性决定了钢筋混凝土墙的破坏结果,爆炸冲击波能够加剧墙体正面开坑和背面崩落的破坏范围;墙体厚度对于墙体正面漏斗坑的直径与深度及内部侵彻孔洞直径均无显著影响;随着墙体厚度增大,背面漏斗坑直径逐渐减小,深度却逐渐增大。     

基于固定角软化桁架模型的钢筋混凝土

在固定角软化桁架模型的基础上,提出了钢筋混凝土构件在纯扭作用下的非线性分析方法。根据平衡条件、变形协调条件和材料本构关系,推导出16个方程,其中包含20个变量。而后根据扭转问题的特点,提出了求解这些方程的有效算法。该方法不仅可以预测受扭构件的极限强度,而且可以预测其开裂后的荷载-变形历史。通过对63个试件的计算验证,计算结果与试验结果吻合良好。     

基于CT扫描的环氧树脂基混凝土裂缝观测与冲击损伤演化研究

环氧树脂基混凝土是一种新型路面铺装材料。本文估算了道路使用过程发生"跳车"现象时货车车轮对路面产生的冲击荷载,根据计算结果,利用落锤冲击试验机对含有不同程度初始损伤的环氧树脂基混凝土试件进行多次冲击试验,研究其冲击疲劳现象。为了准确描述环氧树脂基混凝土的初始损伤,采用CT(计算机断层)扫描技术重构了试件的立体图像,对其中的内部裂缝进行了统计,建立了初始损伤裂缝体积占试件体积的百分比与基于材料弹性模量衰减的损伤变量之间的关系。通过追踪经受一定次数冲击后试件的弹性模量,分析了不同程度初始损伤下环氧树脂基混凝土的冲击损伤随冲击次数的变化规律;结合多次冲击荷载下环氧树脂基混凝土弹性模量的衰减,研究了初始损伤对环氧树脂基混凝土冲击疲劳过程中损伤演化规律的影响。     

Hybrid approach for two dimensional damage localization using piezoelectric smart aggregates

In the paper, a novel approach for damage localization in reinforced concrete plates, based on the computational analysis of piezoelectric smart aggregates, has been presented. The hybrid approach for damage localization is based on two criteria: wave propagation energy and time of flight. The comprehensive numerical analysis using standard and explicit finite element method has been conducted. In addition, the proposed algorithm of the hybrid method has been coded in MATLAB. The approach has been verified numerically using different square reinforced concrete plate models, considering different number, position and size of damage, as well as different number and position of the piezoelectric smart aggregates. Obtained results confirm the successful application of the novel approach to the damage localization.     

一个新的钢筋混凝土损伤塑性模型

为了准确、高效地对拆除爆破工程进行数值模拟,考虑钢筋混凝土受拉刚化效应以及配筋率对受拉刚化效应的影响和受压箍筋约束效应,采用组合模量的方法给出了一个简化的钢筋混凝土本构关系,在LS-DYNA有限元软件中的混凝土损伤塑性模型的基础上,通过参数修改建立新的钢筋混凝土损伤塑性模型模拟来钢筋混凝土。在实验验证的基础上,采用钢筋混凝土损伤塑性等效模型对一双切口钢筋混凝土烟囱延时爆破拆除效果进行数值模拟,数值模拟结果表明该模型可以准确反映烟囱倒塌破坏及运动过程。     

基于能量耗散分析的混凝土随机疲劳损伤模型

基于微-细观随机断裂模型(MMSF)发展了一类混凝土随机疲劳损伤模型。该模型将MMSF中的微弹簧视为一能量耗散单元并考察了其跨尺度的能量耗散过程。在纳观尺度,引入速率过程理论描述裂纹的扩展速度,并基于裂纹层级模型和自相似假定完成从纳观尺度到微观尺度的过渡。由此建立了微弹簧在疲劳荷载作用下的多尺度耗能描述。此外,为了考虑疲劳加载中混凝土多条裂纹的相互影响,引入了包含损伤扩展效应和损伤愈合效应的疲劳损伤因子来修正耗能表达。通过与相关试验的对比,证明了该模型能反映疲劳荷载作用下混凝土的主要力学行为,如疲劳损伤三阶段特点、疲劳寿命的离散性和疲劳寿命随加载频率的变化趋势等。     

Analysis and modelling of the cohesion strength of concrete at high strain-rates

With the exponential increase of computational power, numerical simulations are more and more used to model the response of concrete structures subjected to dynamic loadings such as detonation near a concrete structural element or projectile-impact. Such loadings lead to intense damage modes resulting from high strain-rate tensile loadings in the concrete structure. However, the modelling of the post-peak tensile response of concrete still remains difficult due to the lack of experimental data at high strain-rates. This work aims at improving the modelling of the softening behaviour of concrete based on the following statement: despite the propagation of unstable cracks in the tested specimen cohesion strength exists in the vicinity of triggered cracks and is driving the whole softening behaviour of concrete. This statement is justified in the present work by means of experiments and Monte-Carlo calculations: firstly, concrete samples have been subjected to a dynamic tensile loading by means of spalling experiments. Several specimens have been recovered in a damaged but unbroken state and have been subsequently loaded in quasi-static tensile experiments to characterise the residual strength and damage level in the sample. In addition, Monte-Carlo simulations have been conducted to clarify the possible influence of cohesion strength in the vicinity of cracks. Finally, the DFH (Denoual–Forquin–Hild) anisotropic damage model has been adapted to take into account the cohesion strength in the damaged zone and to describe the softening behaviour of concrete. Numerical simulations of experiments conducted on dry and saturated samples at different levels of loading-rate illustrate the new capability of the model.     

MULTI-SCALE NUMERICAL MODEL FOR SIMULATING CONCRETE MATERIAL BASED ON FRACTAL THEORY

A new multi-scale numerical model is presented using the fractal theory and adopting FEM to simulate the failure of concrete.The relation between the fractal box dimension in large scale and the damage to concrete in small scale is deduced.And the evolutionary process of elastic modulus and strength in small scale is given.Consequently,the multi-scale numerical model is proposed to describe the constitutive relation of concrete between small scale and large scale.A two-dimensional static analysis of a concrete block is performed by using this model and the calculation result is discussed.The propagation of cracks of the concrete block is also studied.     

钢筋锈胀引发混凝土保护层开裂破坏的细观数值研究

钢筋锈蚀膨胀引起保护层混凝土开裂是影响钢筋混凝土结构耐久性和服役寿命的重要因素。考虑到混凝土细观结构组成对保护层破坏模式的影响,从细观角度出发,将混凝土看作由骨料、砂浆基质及两者间界面过渡区组成的三相复合材料,建立了描述钢筋锈胀力学行为的混凝土随机骨料模型。采用塑性损伤本构关系模型来表征砂浆基质和过渡区界面的力学行为,假定钢筋均匀锈蚀,对钢筋锈胀引起的混凝土保护层开裂破坏过程进行了细观数值研究。对比了宏观均匀模型与细观非均质模型下获得的保护层破坏模式,探讨了径厚比(c/d)、钢筋位置(中部和角区)及混凝土拉伸强度对保护层破坏模式及保护层胀裂时钢筋锈蚀水平的影响,得到了一些有益结论。     

半刚接钢框架内填暗竖缝混凝土剪力墙结构的简化滞回分析模型Composite inclined strut hysteretic model for partially-restrained steel frame with concealed vertical slit reinforced concrete infill walls

为解决半刚接钢框架内填暗竖缝混凝土剪力墙结构（简称PSRCW ）在工程应用中的数值分析问题,根据PSRCW结构试验所获得的破坏模式、钢筋混凝土（RC ）墙的裂缝分布规律和结构传力机理,提出了可用于分析PSRCW结构抗震性能的组合斜压带滞回模型。暗竖缝RC墙组合斜压带滞回模型主要由两部分构成。（1）主对角斜压带部分,用于模拟暗竖缝对PSRCW结构水平承载力的贡献。（2）壁柱部分,用于模拟缝间墙的力学行为。基于暗竖缝RC墙的受力机理推导了主对角斜压带的有效宽度计算方法,并结合混凝土的应力‐应变关系给出了主对角斜压带的滞回恢复力模型。采用组合斜压带模型模拟了已有的典型试验,并与试验结果进行了比较,两者吻合较好,进一步证实了本文所提出的组合斜压带滞回模型的合理性。     

基于均匀荷载面曲率的简支裂纹梁损伤识别

为了采用模态参数对结构裂纹进行定位与定量,基于集中柔度模型,采用无质量的扭转弹簧模拟裂纹,建立简支裂纹梁的振动微分方程。针对现有柔度曲率指标仅能判断裂纹的大致范围,基于线性插值理论,建立裂纹位置与相邻测点均匀荷载面曲率差的关系,提出裂纹进一步定位公式,实现裂纹位置的精确定位。针对现有大多数损伤识别方法无法实现裂纹的损伤定量,基于位移曲率与结构刚度和弯矩的关系,理论推导了均匀荷载面曲率的结构刚度损伤程度识别方法,基于弹簧串联原理和线刚度思想,首次提出串联等效线刚度模型,建立裂纹深度与均匀荷载面曲率的关系,实现裂纹深度的定量。通过简支裂纹梁数值算例,考虑多裂纹的损伤情况,验证了新方法对裂纹定位与定量的有效性。