Multivariate Adaptive Regression Splines Model to Predict Fracture Characteristics of High Strength and Ultra High Strength Concrete Beams

This paper presents Multivariate Adaptive Regression Splines (MARS) model to predict the fracture characteristics of high strength and ultra high strength concrete beams. Fracture characteristics include fracture energy (GF), critical stress intensity factor (KIC) and critical crack tip opening displacement (CTODc). This paper also presents the details of development of MARS model to predict failure load (Pmax) of high strength concrete (HSC) and ultra high strength concrete (UHSC) beam specimens. Characterization of mix and testing of beams of high strength and ultra strength concrete have been described. Methodologies for evaluation of fracture energy, critical stress intensity factor and critical crack tip opening displacement have been outlined. MARS model has been developed by establishing a relationship between a set of predicators and dependent variables. MARS is based on a divide and conquers strategy partitioning the training data sets into separate regions; each gets its own regression line. Four MARS models have been developed by using MATLAB software for training and prediction of fracture parameters and failure load.MARS has been trained with about 70% of the total 87 data sets and tested with about 30% of the total data sets. It is observed from the studies that the predicted values of Pmax, GF, KIC and CTODC are in good agreement with those of the experimental values.     

Evaluation of Fracture Parameters by Double-G,Double-K Models and Crack Extension Resistance for High Strength and Ultra High Strength Concrete Beams

This paper presents the advanced analytical methodologies such as Double- G and Double - K models for fracture analysis of concrete specimens made up of high strength concrete (HSC, HSC1) and ultra high strength concrete. Brief details about characterization and experimentation of HSC, HSC1 and UHSC have been provided. Double-G model is based on energy concept and couples the Griffith's brittle fracture theory with the bridging softening property of concrete. The double-K fracture model is based on stress intensity factor approach. Various fracture parameters such as cohesive fracture toughness (K_Ic^c), unstable fracture toughness (K_Ic^un) and initiation fracture toughness (K_Icⁱⁿⁱ) have been evaluated based on linear elastic fracture mechanics and nonlinear fracture mechanics principles. Double-G and double-K method uses the secant compliance at the peak point of measured P-CMOD curves for determining the effective crack length. Bi-linear tension softening model has been employed to account for cohesive stresses ahead of the crack tip. From the studies, it is observed that the fracture parameters obtained by using double - G and double - K models are in good agreement with each other. Crack extension resistance has been estimated by using the fracture parameters obtained through double - K model. It is observed that the values of the crack extension resistance at the critical unstable point are almost equal to the values of the unstable fracture toughness K_Ic^un of the materials. The computed fracture parameters will be useful for crack growth study, remaining life and residual strength evaluation of concrete structural components.     

黏聚裂纹阻抗的弯曲梁承载力

在混凝土类软化材料断裂研究中,裂纹端部损伤区被简化为具有黏聚应力分布的非线性裂纹,该黏 聚力对裂纹扩展有阻抗作用。裂纹体的应力强度因子是断裂力学标志载荷作用与几何构型因素的量化表达指标; 黏聚力形成的阻抗强度因子数值,与黏聚裂纹长度和材料极值拉伸应力存在数量关系。通过双K断裂判据,以 带切口的三点弯曲梁为断裂力学模型,分析了裂纹黏聚阻力对断裂过程的影响规律,计算该弯曲梁结构断裂试 样的最大承担载荷;其结果比较符合实验数据。     

ANN Model to Predict Fracture Characteristics of High Strength and Ultra High Strength Concrete Beams

This paper presents fracture mechanics based Artificial Neural Network (ANN) model to predict the fracture characteristics of high strength and ultra high strength concrete beams. Fracture characteristics include fracture energy (Gf), critical stress intensity factor (KIC) and critical crack tip opening displacement (CTODc). Failure load of the beam (Pmax) is also predicated by using ANN model. Characterization of mix and testing of beams of high strength and ultra strength concrete have been described. Methodologies for evaluation of fracture energy, critical stress intensity factor and critical crack tip opening displacement have been outlined. Back-propagation training technique has been employed for updating the weights of each layer based on the error in the network output. Levenberg- Marquardt algorithm has been used for feed-forward back-propagation. Four ANN models have been developed by using MATLAB software for training and prediction of fracture parameters and failure load. ANN has been trained with about 70% of the total 87 data sets and tested with about 30% of the total data sets. It is observed from the studies that the predicted values of Pmax, Gf, failure load, KIc and CTODc are in good agreement with those of the experimental values.     

Influence of concrete strength and confinement method on axial compressive behavior of FRP confined high- and ultra high-strength concrete

This paper presents an experimental investigation on the effect of concrete compressive strength and confinement method on confined high and ultra high-strength concrete (HSC and UHSC) specimens. A total of 55 fiber reinforced polymer (FRP) confined concrete specimens were tested under monotonic axial compression. All specimens were cylinders with 152 mm diameter and 305 mm height and confined by carbon FRP (CFRP). Three different concrete mixes were examined, with average compressive strengths of 35, 65 and 100 MPa. The effect of the confinement method was also examined with FRP-wrapped specimens compared to FRP tube-encased specimens. Axial and lateral behavior was recorded to observe the axial stress–strain relationship and lateral strain behavior for concentric compression. Ultimate axial and lateral conditions are tabulated and the complete stress–strain curves have been provided. The experimental results presented in this paper provide a performance comparison between FRP-confined conventional normal-strength concrete (NSC) and the lesser understood area of FRP-confined HSC and UHSC. The results of this experimental study clearly indicate that above a certain confinement threshold, FRP-confined HSC and UHSC exhibits highly ductile behavior, however for the same normalized confinement pressures, axial performance of FRP-confined concrete reduces as concrete strength increases. The results also indicate that ultimate conditions of FRP-wrapped specimens are similar to those confined by FRP tubes, however a performance difference is evident at the transition region. The performance of 10 existing stress–strain models were assessed against the experimental datasets and the performance of these models discussed. The results of this model assessment revealed the need for further development for stress–strain models developed specifically for FRP-confined HSC or UHSC.     

小尺寸混凝土试件双K断裂参数试验研究

采用最大尺寸为680mm×160mm×40mm的标准三点弯曲梁试件,利用在初始裂缝两侧粘贴电阻应变片并利用混凝土裂缝扩展到此处时其应变回缩的方法测得了起裂荷载Pini,在此基础上根据Pini及初始缝长a0得到了起裂断裂韧度KIiCni;根据在试验中测得的最大荷载Pmax及对应的裂缝口张开位移CMODC计算了混凝土等效裂缝长度aC,据此计算了失稳断裂韧度KIuCn。结果表明:采用电阻应变片法可准确测定混凝土的起裂荷载Pini,且方法简单。试验结果还表明:在本试验范围内,三点弯曲梁法测得的混凝土双K断裂参数KIiCni、KIuCn与试件高度无关,进一步说明了混凝土双K断裂参数可以作为描述混凝土裂缝扩展的断裂参数。     

基于虚拟裂缝模型的混凝土等效断裂韧度

本文采用虚拟裂缝模型,将临界裂缝尖端张开位移ＣＴＯＤｃ作为控制参数,利用三点弯曲梁试件通过迭代求得了混凝土裂缝亚临界扩展量的临界值△ａｃ,据此求得了混凝土起裂断裂韧度ＫｉｎｉＩｃ、等效断裂韧度ＫｕｎＩｃ值。计算结果表明,随着试件尺寸的增大,△ａｃ增大,但ＫｉｎｉＩｃ、ＫｕｎＩｃ值却是与试件尺寸无关的断裂参数。这表明线弹性断裂韧度准则可应用于混凝土结构的裂缝评定。     

A finite fracture mechanics approach to structures with sharp V-notches

Criteria assuming that failure of quasi-brittle materials is affected by the stresses acting over a finite distance from the crack tip are widely used inside the scientific community. For instance, they have been applied to predict the failure load of specimens containing sharp V-notches, assuming as a critical parameter the average stress ahead the notch tip. However, this kind of approaches disregards energy balance considerations, which, as well known, are the basis of linear elastic fracture mechanics (LEFM). In order to overcome these drawbacks, the present paper uses a recently introduced finite fracture mechanics (FFM) criterion, i.e. a fracture criterion assuming that crack grows by finite steps. The length of this finite extension is determined by a condition of consistency of both energy and stress requirements; as a consequence, the crack advancement is not a material constant but a structural parameter. The criterion is applied to structures with sharp V-notches. The expression of the generalized fracture toughness, which is a function of material tensile strength, fracture toughness and notch opening angle, is given analytically. Finally, we provide comparisons with: (i) the experimental data we obtained from testing Polystyrene specimens under three point bending; (ii) some experimental data available in the literature. The agreement between theoretical predictions and experimental results is generally satisfactory and, for most of the cases analyzed, the FFM predictions are better than the ones provided by the simple average stress approach.     

Delamination of thin bonded cement-based overlays: analytical analysis

This paper deals with an analytical approach for the prediction of debonding initiation between cement-based overlay and old concrete substrate under monotonous mechanical loading. Based on the linear elastic fracture mechanics, an available analytical model has been used. The calculations take into account the interlocking between two crack surfaces in the overlay. To validate the model, three point static bending tests on composite specimens were carried out. Assuming that the debonding initiation just occurs after the crack cutting the overlay layer reaches the overlay–substrate interface, the stress intensity factor of the debonding tip can be calculated, allowing prediction of stress fields near the interface debonding tip. Then with a criterion of debonding initiation and propagation depending on the interface tensile strength, the load associated could be determined and might be interesting for the design of thin bonded cement-based overlays. The adequateness of this analytical approach was verified by both experimental data and finite element calculations.     

Structural Performance of Precast and Cast-in-situ Ultra High Strength Concrete Sandwich Panel

This paper investigates the flexural performance of a sandwich panel made up of ultra high strength concrete (UHSC) as top and bottom skin and cold formed steel as sandwich. A novel sandwich panel has been designed such a way that bottom skin of UHSC is of precast in nature and top skin of UHSC is cast-insitu and cold formed steel (profiled sheet) as sandwich. The connection between top skin of UHSC and cold formed steel is made with self tapping screws. Flexural performance of UHSC sandwich panel has been tested under flexural loading and it is found that the post peak response of the panel is significant in terms of more energy absorption. It is observed that the final failure of the specimen is occurred by forming a dominant crack on the bottom face of the skin apart formation of many multiple cracks with increase of load. Numerical investigations have been carried out by simulating the experimental conditions and found that the response obtained through simulation is in good agreement with the corresponding experimental values. From the studies, it can be concluded that UHSC steel sandwich panels can be employed for structural and non structural applications.     

Finite fracture mechanics: A coupled stress and energy failure criterion

The aim of the present paper is to introduce a new failure criterion in the framework of Finite Fracture Mechanics. Criteria assuming that failure of quasi-brittle materials is affected by stress or energy flux acting on a finite distance in front of the crack tip are widely used inside the scientific community. Generally, this distance is assumed to be small compared to a characteristic size of the structure, i.e. to any length describing the macroscale. A key point of the present paper is to analyse what happens if the smallness assumption does not hold true. The proposed approach relies on the assumption that the finite distance is not a material constant but a structural parameter. Its value is determined by a condition of consistency of both energetic and stress approaches. The model is general. In order to check its soundness, an application to the strength prediction for three point bending tests of various relative crack depths and of different sizes is performed. It is seen that, for the un-notched specimens, the present model predicts the same trend as the Multi-Fractal Scaling Law (MFSL). Finally, a comparison with experimental data available in the literature on high strength concrete three point bending specimens is performed, showing an excellent agreement. It is remarkable to observe that the method presented herein is able to provide the fracture toughness using test data from un-notched specimens, as long as the range of specimen sizes is broad enough.     

用能量方法研究混凝土断裂过程区的力学性能

准脆性混凝土自由裂缝前缘断裂过程区的发展与其非线性断裂特征及尺寸效应现象密切相关。它的物理力学行为的量化分析对理解混凝土断裂破坏机理和建立适用于混凝土结构裂缝稳定分析和安全评估断裂准则尤为重要,一直是混凝土断裂力学研究的核心问题。该文依据Hillerborg给出的断裂能定义,给出了计算单位长度断裂过程区发展能量耗散的通用表达式。以三点弯曲梁为例,采用非线性软化本构关系,进一步给出了计算此平均能量耗散的具体步骤及对应的公式。在根据实测的三点弯曲梁的断裂能回归拟合了特征裂缝张开位移w0后,计算了每个试件整个断裂全过程中不同荷载时刻断裂过程区耗能的平均值。结果表明:随着裂缝扩展,断裂过程区能量耗散的变化和试件尺寸无关,可描述断裂过程区混凝土材料的力学性能。     

ANALYSIS AND MODELISATION OF SHORT CRACK GROWTH BY DUCTILE FRACTURE MICROMECHANISMS

Abstract— A ductile medium strength steel has been modelled by means of the Gurson model, and been used to investigate the effect of crack tip constraint in several fracture mechanics specimens. Both numerical and experimental results have been obtained, in the course of the crack extension process, for single edge notch bending specimens with different crack length-to-width ratios. The geometries with the shorter cracks always exhibited higher J values at initiation and steeper J crack growth resistance curves, and these results have been explained in terms of the stress and strain fields and damage development in the region ahead of the crack tip.     

Fracture stability and residual strength assessment of reinforced concrete beams

In conventional analysis and design procedures of reinforced concrete structures, the ability of concrete to resist tension is neglected. Under cyclic loading, the tension-softening behavior of concrete influences its residual strength and subsequent crack propagation. The stability and the residual strength of a cracked reinforced concrete member under fatigue loading, depends on a number of factors such as, reinforcement ratio, specimen size, grade of concrete, fracture properties, and on the tension-softening behavior of concrete. In this work, a method is proposed to assess the residual strength of reinforced concrete beams subjected to cyclic loading. The crack extension resistance based approach is used for determining the condition for unstable crack propagation. The effect of reinforcement is modeled as a closing force counteracting the effect of crack opening produced by the external moment. The effect of percentage reinforcement and specimen size on the failure of reinforced beams is studied. Finally, the residual strength of the beams are computed by including the softening behavior of concrete.     

Two-layer pre-stressed beams consisting of normal and steel fibered high strength concrete

The paper is focused on analysis of two-layer bending pre-stressed beams consisting of steel fibered (SF) high strength concrete (HSC) in compressed zone and normal strength concrete (NSC) in tensile zone. Investigation of such beams is important for RC structural design, because calculation of fibers volume ratio is significant, like that of reinforcing steel bars for usual RC elements. In other words, such elements are made of high performance concrete (HPC). There is a growing tendency that more effective HPC structures replace NSC ones, first of all in pre-stressed elements. Definition of the HSC class lower limit, to be used in the compressed zone of a two-layer pre-stressed beam, is given. It was demonstrated that SF have little effect on the beam elastic deflections. However, the ultimate deflections of the section increase because additional potential for plastic energy dissipation (PED) in the bending element. NSC, used in the section tensile zone, contributes additionally about 20% to the section’s PED potential compared to one-layer HSC beams. In order to guarantee sufficient section’s ductility of the pre-stressed beams, required to withstand dynamic loadings, a minimum SF ratio is proposed to be considered. The fibers take the tensile stresses, yielding cracks in the concrete matrix. A design method for calculation of the SF volume ratio, as a function of required ductility, is proposed. A numerical example, illustrating the efficiency of this method is presented.     

混凝土I型裂缝扩展准则比较研究

针对混凝土I型裂缝扩展问题,分别采用以起裂韧度为参数的裂缝扩展准则、最大拉应力准则以及裂尖处应力强度因子为零的裂缝扩展准则,数值模拟了强度等级C20、C40、C60、C80和C100的混凝土三点弯曲梁裂缝扩展全过程,获取了试件的荷载-裂缝口张开位移(P-CMOD)曲线并与试验结果进行了比较。结果表明,三种准则中以起裂韧度为参数的裂缝扩展准则计算得到的峰值荷载及P-CMOD全曲线与试验结果差别最小。随着混凝土强度等级的提高,最大拉应力准则以及裂尖处应力强度因子为零的裂缝扩展准则计算出的P-CMOD曲线与试验结果相比均有较为明显的偏离,但以起裂韧度为参数的裂缝扩展准则计算结果与试验曲线更为吻合。试验与计算结果表明,以起裂韧度为参数的裂缝扩展准则更适用于不同强度混凝土材料的断裂分析。     

Implications of test methodology on post-cracking and fracture behaviour of Steel Fibre Reinforced Concrete

It is now universally recognized that the mechanical, cracking and fracture, properties of Steel Fibre Reinforced Concrete (SFRC) are far superior to those of plain concrete. The use of SFRC contributes effectively to preserve the structural stability and structural integrity of concrete elements and improve their ductile behaviour.To optimize the performance of SFRC in structural members it is necessary to establish the mechanical properties very precisely. The best test methodology to evaluate the post-cracking and toughness properties of SFRC is the beam bending test. Design codes recommend one of two bending test configurations: the three-point or the four-point bending test. The results obtained from these two test configurations are not identical.The overall focus of this paper is to evaluate the contributions of fibres to the post-cracking and fracture behaviour of concrete as determined by the two different standard test procedures. To achieve these aims plain and fibre concrete specimens were tested. All the test specimens were extensively instrumented to establish the strength properties, crack tip and crack mouth opening displacement, post-cracking and fracture behaviour. The results of the two types of bending tests were then critically analysed and evaluated to identify the differing effects of the bending load configurations on material and structural behaviour.SFRC specimens subjected to four-point bending test showed higher stress values compared to those obtained from the three-point bending tests. The first crack strength values evaluated following the two standards are close with an improvement of 10% for the European standard.     

Residual strength of unidirectional fibre-metal laminates based on JC toughness of C(T) and SE(B) specimens: comparison with M(T) test results

Fibre‐metal laminates (FMLs) are structural composites designed with the aim of producing very low fatigue crack‐propagation rate, damage‐tolerant and high‐strength materials, if compared to aeronautical Al alloys. Their application in aeronautical structures demands a deep knowledge of a wide set of mechanical properties and technological values, including both fracture toughness and residual strength. The residual strength of FMLs have been traditionally determined by using wide centre‐cracked tension panels M(T). The use of this geometry requires large quantities of material and heavy laboratory facilities. In this work, fracture toughness ( J_C) of some unidirectional FMLs laminates was measured using a recently proposed methodology for critical fracture toughness evaluation on compact tension C(T) and single‐edge bend SE(B) specimens. Additionally, residual strength values of wider M(T) specimens with different widths (W from 150 to 200 mm) and several crack to width ratios (2a/W) were experimentally obtained. Some experimental residual strength values of M(T) specimens (W from 150 to 400 mm and different 2a/W ratios) of Arall were also obtained from the bibliography. Based on J_C results from C(T) and SE(B) specimens, and either using or not using crack‐tip plasticity corrections, the residual strengths of the M(T) specimens were predicted and compared to the experimental ones. The results showed good agreement, especially when crack‐tip plasticity corrections were applied.     

Determination of the kink point in the bilinear softening model for concrete

The characterization of the softening curve from experimental results is essential for predicting the fracture behavior of quasi-brittle materials like concrete. Among various shapes (e.g. linear, exponential) to describe the softening behavior of concrete, the bilinear softening relationship has been extensively used and is the model of choice in this work. Currently, there is no consensus about the location of the kink point in the bilinear softening curve. In this study, the location of the kink point is proposed to be the stress at the critical crack tip opening displacement. Experimentally, the fracture parameters required to describe the bilinear softening curve can be determined with the “two-parameter fracture model” and the total work of fracture method based on a single concrete fracture test. The proposed location of the kink point compares well with the range of kink point locations reported in the literature, and is verified by plotting stress profiles along the expected fracture line obtained from numerical simulations with the cohesive zone model. Finally, prediction of experimental load versus crack mouth opening displacement curves validate the proposed location of the kink point for different concrete mixtures and also for geometrically similar specimens with the same concrete mixture. The experiments were performed on three-point bending specimens with concrete mixtures containing virgin coarse aggregate, recycled concrete coarse aggregate (RCA), and a 50-50 blend of RCA and virgin coarse aggregate. The verification and validation studies support the hypothesis of the kink point occurring at the critical crack tip opening displacement.     

Experimental and numerical investigations on fracture process zone of rock–concrete interface

A crack propagation criterion for a rock–concrete interface is employed to investigate the evolution of the fracture process zone (FPZ) in rock–concrete composite beams under three‐point bending (TPB). According to the criterion, cracking initiates along the interface when the difference between the mode I stress intensity factor at the crack tip caused by external loading and the one caused by the cohesive stress acting on the fictitious crack surfaces reaches the initial fracture toughness of a rock–concrete interface. From the experimental results of the composite beams with various initial crack lengths but equal depths under TPB, the interface fracture parameters are determined. In addition, the FPZ evolution in a TPB specimen is investigated by using a digital image correlation technique. Thus, the fracture processes of the rock–concrete composite beams can be simulated by introducing the initial fracture criterion to determine the crack propagation. By comparing the load versus crack mouth opening displacement curves and FPZ evolution, the numerical and experimental results show a reasonable agreement, which verifies the numerical method developed in this study for analysing the crack propagation along the rock–concrete interface. Finally, based on the numerical results, the effect of ligament length on the FPZ evolution and the variations of the fracture model during crack propagation are discussed for the rock–concrete interface fracture under TPB. The results indicate that ligament length significantly affects the FPZ evolution at the rock–concrete interface under TPB and the stress intensity factor ratio of modes II to I is influenced by the specimen size during the propagation of the interfacial crack.