基于断裂力学的钢筋、FRP与混凝土界面力学特性研究
摘要
随着混凝土锚固与加固技术的推广和应用,补强材料与混凝土界面粘结问题逐渐引起了国内外学者们的普遍关注。本论文采用断裂力学方法研究钢筋、FRP(纤维增强复合材料)与混凝土界面力学特性,主要针对钢筋-砂浆-混凝土三相介质锚固体和CFRP(碳纤维增强复合材料)布加固混凝土弯曲梁两个问题,分别进行研究。具体工作如下:
(1)首先提出了一个计算混凝土等效断裂韧度的解析模型。利用该模型,只要测得混凝土的弹性模量和抗折强度,就可以计算临界等效裂缝长度和极限荷载,进而求得混凝土等效断裂韧度,在此基础上研究了等效断裂韧度的尺寸效应。
(2)针对少筋混凝土三点弯曲切口梁断裂问题,采用虚拟裂缝模型以及钢筋与混凝土界面变形协调条件提出了计算极限荷载的解析方法,考虑了钢筋不屈服界面发生粘结滑移和钢筋屈服界面不发生粘结滑移两种情况。结果表明,加载过程中荷载将出现两个峰值,而对于钢筋发生屈服的情况,第二个峰值对应的是钢筋刚刚发生屈服时的荷载,该种情况下两峰值的计算结果得到了试验验证。因此采用该解析模型,只要测得混凝土的抗折强度、弹性模量以及钢筋的屈服强度,就可以计算不同缝高比的钢筋混凝土少筋梁在钢筋发生屈服时的承载力。
(3)针对钢筋-砂浆-混凝土三相介质锚固体发生界面粘结破坏的情况,根据界面变形协调条件和砂浆层的剪切变形协调条件得到了砂浆层剪应力沿砂浆层厚度方向的分布,以及钢筋拉应力和两界面剪应力的表达式。根据两界面粘结强度、钢筋直径和砂浆层厚度判断了两界面发生粘结破坏的可能性;针对钢筋与砂浆界面发生粘结破坏和两界面均发生粘结破坏两种情况下的钢筋极限抗拔力进行研究。将界面粘结破坏过程作为剪切裂缝扩展,对锚固体不同边界约束条件下裂缝在钢筋加载端界面和自由端界面出现的可能性和先后顺序进行判断,建立了拔出荷载和裂缝长度的关系,并通过极值理论求得极限荷载和对应的临界裂缝长度。并研究了钢筋锚固长度、混凝土刚度、砂浆层厚度以及界面参数对计算结果的影响。
(4)当锚固体破坏型式为砂浆层剪切破坏时,根据界面变形协调条件和砂浆层剪切变形协调条件,得到了钢筋拉应力和砂浆层剪应力的表达式。针对锚固体不同边界约束条件下砂浆层剪切裂缝在钢筋加载端和自由端出现的可能性和先后顺序进行判断,建立了荷载和剪切裂缝长度之间的关系,进而利用极值理论求得极限荷载和对应的临界裂缝长度。参数研究中分析了钢筋锚固长度、混凝土刚度、砂浆剪切模量和剪切断裂能对计算结果的影响。
(5)针对锚固体中混凝土锥形破坏和界面粘结破坏均发生的情况提出了一个解析方法,研究了两种破坏之间的影响以及两种破坏出现的可能性和先后顺序,分析了不同锚固长度、混凝土刚度、砂浆层厚度和混凝土抗拉强度对锚固体破坏型式的影响。
(6)作为问题的一个推广,还针对锚筋从灌注于钢管内的砂浆中拔出问题,利用锚筋与砂浆界面的变形协调条件和砂浆层剪切变形协调条件提出了一个计算锚筋极限抗拔力的解析模型,并得到了试验验证。因此,只需确定锚筋与砂浆界面的四个特征参数,并结合锚筋、砂浆和钢管的弹性模量,就可以计算相同结构型式不同尺寸锚固体中锚筋的极限抗拔力。
(7)针对CFRP布加固的混凝土三点弯曲切口梁,基于虚拟裂缝模型和界面变形协调条件提出一个解析方法,研究混凝土跨中垂直裂缝和界面水平裂缝扩展共同作用对梁承载力的影响。分析结果表明,加载过程中荷载出现两个峰值,且两峰值的计算结果得到了试验验证。采用该解析模型,只需CFRP布与混凝土界面的三个特征参数、混凝土和CFRP布的弹性模量及混凝土的抗折强度,就可以计算不同初始缝高比CFRP布加固的混凝土梁的承载力。
As the techniques are widely developed and applied in fields of anchorage and rehabilitation for concrete, researchers have gradually paid more attention to bond properties between repairing materials and concrete. The present study aims at the mechanical behaviors at both the tendon-concrete and FRP (fiber-reinforced polymer) -concrete interfaces based on fracture mechanics. Two models are mainly analyzed, namely, tendon-mortar-concrete anchorage and CFRP (carbon fiber-reinforced polymer) sheet strengthened three-point bending notched beam of concrete. Details of the present study are introduced as follows.
(1) First, an analytical model is presented to calculate the effective fracture toughness of concrete. Only if the elastic modulus and flexural tensile strength of the concrete are given, the critical effective crack length and maximum applied load can be predicted by using the proposed model. Then the size effects of the effective fracture toughness are studied.
(2) An analytical method is proposed to predict the load carrying capacity of three-point bending notched beams of lightly reinforced concrete based on the fictitious crack model and deformation compatibility conditions at the steel bar-concrete interface. Two cases are considered. Case 1 allows interfacial debonding at the steel bar-concrete interface without yielding of the steel bar and Case 2 means the steel bar can yield without interfacial debonding. Results show that there are two peak values of the applied load during the loading stage. And the second peak value is corresponding to the initiation of steel bar yielding in Case 2. Then the calculated two peak values in Case 2 are verified with experimental results. Therefore, when the elastic modulus and flexural tensile strength of the concrete, and the yielding strength of the steel bar, are given, the loading carrying capacity can be predicted for lightly reinforced concrete beams with different ratios of initial notch length to beam height in Case 2.
(3) When interfacial debonding failure occurs in the tendon-mortar-concrete anchorage, the variations of shear stresses along the thickness of the mortar layer are obtained based on the deformation compatibility conditions at the two interfaces and shear deformation compatibility conditions in the mortar layer. Then the expressions of tensile stress in the tendon and interfacial shear stress are yielded. The possibilities of interfacial debonding at the two interfaces are judged according to the two interfacial shear strengths, diameter of the tendon and thickness of the mortar. Only the interfacial debonding at the tendon-mortar interface and the interfacial debonding at both of the two interfaces are studied, respectively, in the present study. Moreover, the interfacial debonding is modeled as the interfacial shear crack propagation. Then the appearance possibilities and orders of the interfacial shear cracks from the loading and free ends of the tendon are judged according to different boundary conditions of the anchorage. The expressions of the pullout load with respect to the interfacial crack lengths are established and the maximum pullout load and critical crack lengths are obtained using theories of extremum. Besides, the effects of the embedment length, concrete rigidity, mortar thickness and interfacial parameters on the calculated results are discussed.
(4) When the failure mode of the anchorage is shear failure of the mortar, the expressions of tensile stress in the tendon and shear stress in the mortar are obtained based on the deformation compatibility conditions at the interfaces and shear deformation compatibility conditions in the mortar layer. The appearance possibilities and orders of the shear cracks in the mortar from the loading and free ends of the tendon are judged according to different boundary conditions of the anchorage. Moreover, the expressions of the pullout load with respect to the shear crack lengths are established and the maximum pullout load and critical shear crack lengths are obtained using theories of extremum. The effects of the embedment length, concrete rigidity, mortar shear modulus and shear fracture energy on the calculated results are discussed.
(5) An analytical method is presented for the anchorage by considering both the concrete cone failure and interfacial debonding. The effects of the two failure modes on each other are studied. Then the appearance possibilities and orders of the two failure modes are judged. Moreover, the effects of the embedment length, concrete rigidity, mortar thickness and concrete tensile strength on the failure modes are analyzed.
(6) The analytical methods for the anchorage are applied to study pullout of an anchor from mortar filled steel tube. Then an analytical method is proposed to predict the maximum pullout load based on the deformation compatibility condition at the anchor-mortar interface and shear deformation compatibility condition in the mortar layer. The calculated tensile capacity is verified with experimental results. Therefore, when four interfacial parameters determining the interfacial behaviors and a few material parameters are given, the maximum pullout load can be predicted for the anchor-mortar-tube anchorage with different sizes.
(7) An analytical method is presented to predict the loading carrying capacity of CFRP sheet strengthened three-point bending notched beams of concrete based on the fictitious crack model and deformation compatibility condition at the CFRP-concrete interface. Both the vertical crack propagation in the concrete and horizontal interfacial shear crack propagation are considered in the proposed model. Results show that there are two peak values of the applied load during the loading stage. Then the calculated two peak values are verified with experimental results. Therefore, when three interfacial parameters determining the interfacial behaviors and a few material parameters are given, the loading carrying capacity can be predicted for CFRP sheet strengthened three-point bending notched beams with different ratios of initial notch length to beam height.
(1)首先提出了一个计算混凝土等效断裂韧度的解析模型。利用该模型,只要测得混凝土的弹性模量和抗折强度,就可以计算临界等效裂缝长度和极限荷载,进而求得混凝土等效断裂韧度,在此基础上研究了等效断裂韧度的尺寸效应。
(2)针对少筋混凝土三点弯曲切口梁断裂问题,采用虚拟裂缝模型以及钢筋与混凝土界面变形协调条件提出了计算极限荷载的解析方法,考虑了钢筋不屈服界面发生粘结滑移和钢筋屈服界面不发生粘结滑移两种情况。结果表明,加载过程中荷载将出现两个峰值,而对于钢筋发生屈服的情况,第二个峰值对应的是钢筋刚刚发生屈服时的荷载,该种情况下两峰值的计算结果得到了试验验证。因此采用该解析模型,只要测得混凝土的抗折强度、弹性模量以及钢筋的屈服强度,就可以计算不同缝高比的钢筋混凝土少筋梁在钢筋发生屈服时的承载力。
(3)针对钢筋-砂浆-混凝土三相介质锚固体发生界面粘结破坏的情况,根据界面变形协调条件和砂浆层的剪切变形协调条件得到了砂浆层剪应力沿砂浆层厚度方向的分布,以及钢筋拉应力和两界面剪应力的表达式。根据两界面粘结强度、钢筋直径和砂浆层厚度判断了两界面发生粘结破坏的可能性;针对钢筋与砂浆界面发生粘结破坏和两界面均发生粘结破坏两种情况下的钢筋极限抗拔力进行研究。将界面粘结破坏过程作为剪切裂缝扩展,对锚固体不同边界约束条件下裂缝在钢筋加载端界面和自由端界面出现的可能性和先后顺序进行判断,建立了拔出荷载和裂缝长度的关系,并通过极值理论求得极限荷载和对应的临界裂缝长度。并研究了钢筋锚固长度、混凝土刚度、砂浆层厚度以及界面参数对计算结果的影响。
(4)当锚固体破坏型式为砂浆层剪切破坏时,根据界面变形协调条件和砂浆层剪切变形协调条件,得到了钢筋拉应力和砂浆层剪应力的表达式。针对锚固体不同边界约束条件下砂浆层剪切裂缝在钢筋加载端和自由端出现的可能性和先后顺序进行判断,建立了荷载和剪切裂缝长度之间的关系,进而利用极值理论求得极限荷载和对应的临界裂缝长度。参数研究中分析了钢筋锚固长度、混凝土刚度、砂浆剪切模量和剪切断裂能对计算结果的影响。
(5)针对锚固体中混凝土锥形破坏和界面粘结破坏均发生的情况提出了一个解析方法,研究了两种破坏之间的影响以及两种破坏出现的可能性和先后顺序,分析了不同锚固长度、混凝土刚度、砂浆层厚度和混凝土抗拉强度对锚固体破坏型式的影响。
(6)作为问题的一个推广,还针对锚筋从灌注于钢管内的砂浆中拔出问题,利用锚筋与砂浆界面的变形协调条件和砂浆层剪切变形协调条件提出了一个计算锚筋极限抗拔力的解析模型,并得到了试验验证。因此,只需确定锚筋与砂浆界面的四个特征参数,并结合锚筋、砂浆和钢管的弹性模量,就可以计算相同结构型式不同尺寸锚固体中锚筋的极限抗拔力。
(7)针对CFRP布加固的混凝土三点弯曲切口梁,基于虚拟裂缝模型和界面变形协调条件提出一个解析方法,研究混凝土跨中垂直裂缝和界面水平裂缝扩展共同作用对梁承载力的影响。分析结果表明,加载过程中荷载出现两个峰值,且两峰值的计算结果得到了试验验证。采用该解析模型,只需CFRP布与混凝土界面的三个特征参数、混凝土和CFRP布的弹性模量及混凝土的抗折强度,就可以计算不同初始缝高比CFRP布加固的混凝土梁的承载力。
As the techniques are widely developed and applied in fields of anchorage and rehabilitation for concrete, researchers have gradually paid more attention to bond properties between repairing materials and concrete. The present study aims at the mechanical behaviors at both the tendon-concrete and FRP (fiber-reinforced polymer) -concrete interfaces based on fracture mechanics. Two models are mainly analyzed, namely, tendon-mortar-concrete anchorage and CFRP (carbon fiber-reinforced polymer) sheet strengthened three-point bending notched beam of concrete. Details of the present study are introduced as follows.
(1) First, an analytical model is presented to calculate the effective fracture toughness of concrete. Only if the elastic modulus and flexural tensile strength of the concrete are given, the critical effective crack length and maximum applied load can be predicted by using the proposed model. Then the size effects of the effective fracture toughness are studied.
(2) An analytical method is proposed to predict the load carrying capacity of three-point bending notched beams of lightly reinforced concrete based on the fictitious crack model and deformation compatibility conditions at the steel bar-concrete interface. Two cases are considered. Case 1 allows interfacial debonding at the steel bar-concrete interface without yielding of the steel bar and Case 2 means the steel bar can yield without interfacial debonding. Results show that there are two peak values of the applied load during the loading stage. And the second peak value is corresponding to the initiation of steel bar yielding in Case 2. Then the calculated two peak values in Case 2 are verified with experimental results. Therefore, when the elastic modulus and flexural tensile strength of the concrete, and the yielding strength of the steel bar, are given, the loading carrying capacity can be predicted for lightly reinforced concrete beams with different ratios of initial notch length to beam height in Case 2.
(3) When interfacial debonding failure occurs in the tendon-mortar-concrete anchorage, the variations of shear stresses along the thickness of the mortar layer are obtained based on the deformation compatibility conditions at the two interfaces and shear deformation compatibility conditions in the mortar layer. Then the expressions of tensile stress in the tendon and interfacial shear stress are yielded. The possibilities of interfacial debonding at the two interfaces are judged according to the two interfacial shear strengths, diameter of the tendon and thickness of the mortar. Only the interfacial debonding at the tendon-mortar interface and the interfacial debonding at both of the two interfaces are studied, respectively, in the present study. Moreover, the interfacial debonding is modeled as the interfacial shear crack propagation. Then the appearance possibilities and orders of the interfacial shear cracks from the loading and free ends of the tendon are judged according to different boundary conditions of the anchorage. The expressions of the pullout load with respect to the interfacial crack lengths are established and the maximum pullout load and critical crack lengths are obtained using theories of extremum. Besides, the effects of the embedment length, concrete rigidity, mortar thickness and interfacial parameters on the calculated results are discussed.
(4) When the failure mode of the anchorage is shear failure of the mortar, the expressions of tensile stress in the tendon and shear stress in the mortar are obtained based on the deformation compatibility conditions at the interfaces and shear deformation compatibility conditions in the mortar layer. The appearance possibilities and orders of the shear cracks in the mortar from the loading and free ends of the tendon are judged according to different boundary conditions of the anchorage. Moreover, the expressions of the pullout load with respect to the shear crack lengths are established and the maximum pullout load and critical shear crack lengths are obtained using theories of extremum. The effects of the embedment length, concrete rigidity, mortar shear modulus and shear fracture energy on the calculated results are discussed.
(5) An analytical method is presented for the anchorage by considering both the concrete cone failure and interfacial debonding. The effects of the two failure modes on each other are studied. Then the appearance possibilities and orders of the two failure modes are judged. Moreover, the effects of the embedment length, concrete rigidity, mortar thickness and concrete tensile strength on the failure modes are analyzed.
(6) The analytical methods for the anchorage are applied to study pullout of an anchor from mortar filled steel tube. Then an analytical method is proposed to predict the maximum pullout load based on the deformation compatibility condition at the anchor-mortar interface and shear deformation compatibility condition in the mortar layer. The calculated tensile capacity is verified with experimental results. Therefore, when four interfacial parameters determining the interfacial behaviors and a few material parameters are given, the maximum pullout load can be predicted for the anchor-mortar-tube anchorage with different sizes.
(7) An analytical method is presented to predict the loading carrying capacity of CFRP sheet strengthened three-point bending notched beams of concrete based on the fictitious crack model and deformation compatibility condition at the CFRP-concrete interface. Both the vertical crack propagation in the concrete and horizontal interfacial shear crack propagation are considered in the proposed model. Results show that there are two peak values of the applied load during the loading stage. Then the calculated two peak values are verified with experimental results. Therefore, when three interfacial parameters determining the interfacial behaviors and a few material parameters are given, the loading carrying capacity can be predicted for CFRP sheet strengthened three-point bending notched beams with different ratios of initial notch length to beam height.
引文
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