钢纤维混凝土静力损伤及疲劳损伤研究
摘要
钢纤维混凝土(SteelFiberReinforcedConcrete,简写为SFRC)是在普通混凝土中掺入乱向分布的短钢纤维所形成的一种新型复合材料。它不仅具有普通混凝土的优良特性，同时由于钢纤维的存在限制了裂缝的开展，从而使原来本质上是脆性的混凝土材料呈现出很高的抗裂性能并能推迟裂缝的出现、使混凝土具有较大的延性和韧性以及优良的抗拉、抗折、抗冲击、耐磨损、抗疲劳等特性。近年来，钢纤维混凝土得到广泛的应用和深入的研究。根据国内外已有的研究成果，本文对钢纤维混凝土静力损伤和疲劳损伤进行了研究，主要研究内容及结论如下：
1、给出了将试验得到的4点弯曲梁的荷载－挠度曲线转化为相应的应力－应变曲线的方法；根据能量等效原理和weibull统计分布理论推导了钢纤维混凝土在单向荷载作用下的本构模型及其损伤模型，只要能准确的测定出试件的弹性模量、峰值应力以及相应的峰值应变，就能得到其单向荷载作用下的本构方程和损伤演变方程。
2、静载破坏可看成是特殊的疲劳破坏，即极限强度加载下，承受一个循环的疲劳破坏。在此过程中，损伤也是一个逐步累积的过程。借鉴疲劳损伤的分析方法，基于损伤力学推导了单轴加载作用下描述损伤变量与应变关系的损伤演变方程。根据应变等效原理，得到对应的本构方程。
3、对钢纤维再生混凝土和钢纤维卵石混凝土弯曲疲劳性能进行了试验研究，得到不同应力水平（S=0.7,0.75,0.8,0.85）下的疲劳寿命。分析结果表明：应力水平S与对数疲劳寿命lgN成直线关系，相关系数在0.99以上，因钢纤维和粗骨料之间的界面连接强度不同，在任何应力水平下钢纤维再生混凝土的疲劳寿命都比钢纤维卵石混凝土大。综合已有文献回归得到的弯曲疲劳载荷作用下的疲劳寿命方程，可作为弯曲疲劳荷载作用下疲劳寿命的估算。钢纤维再生混凝土和钢纤维卵石混凝土弯曲疲劳应变演化曲线呈现三阶段发展规律，随着循环比的增加，钢纤维再生混凝土的疲劳应变比钢纤维卵石混凝土的疲劳应变发展慢。由此可见，利用再生骨料作为粗骨料的钢纤维再生混凝土不仅能“变废为宝”，减少环境污染，实现资源的重复利用，而且其疲劳寿命和疲劳应变发展都优于钢纤维卵石混凝土。
4、利用威布尔分布和对数正态分布对钢纤维再生混凝土和钢纤维卵石混凝土的疲劳寿命试验结果进行检验，结果表明本次试验的弯曲疲劳寿命较好地服从对数正态分布和两参数威布尔分布。不同存活率P和应力水平S下，单对数疲劳方程和双对数疲劳方程的线性关系是成立的，其相关系数R均在0.99以上；存活率P对钢纤维卵石混凝土的回归系数B和b影响很小，可取其平均值作为通用结果，而存活率P对钢纤维卵石混凝土各回归系数影响很小，可取其平均值作为通用结果。
5.通过对二级配钢纤维混凝土疲劳试验数据进行回归，提出了二级配钢纤维混凝土弯曲疲劳方程，其回归系数可以达到0.971以上，比采用其他拟合公式更接近试验结果。
6.提出了描述钢纤维混凝土的疲劳应变演化曲线的疲劳应变方程，结果显示，拟合曲线与试验曲线能很好吻合。根据疲劳模量与疲劳应变幅值成反比的关系，由疲劳应变演化方程得到疲劳模量演化方程。利用疲劳模量演化方程对已有疲劳模量试验结果进行拟合，结果显示，该式表达的疲劳模量演化曲线与相应的试验曲线吻合很好，其相关系数均在0.99以上，说明该式适合描述钢纤维混凝土的疲劳模量演化曲线。
7、分别用疲劳应变和疲劳模量定义钢纤维混凝土疲劳损伤，得到的典型的损伤变量演化曲线显示，由最大疲劳应变和疲劳残余应变定义的损伤变量演化曲线基本一致，且相差很小；而由疲劳模量定义的损伤变量演化曲线明显大于由疲劳应变定义的损伤变量演化曲线，当循环比为0.9时，由疲劳应变定义的损伤变量约0.35左右，而疲劳模量定义的损伤变量约为0.77，当初始循环时，疲劳模量定义的损伤变量就达到0.34左右，而疲劳应变定义的损伤变量接近0。也就是说，由疲劳模量定义的损伤变量自始至终都比疲劳应变定义的损伤变量大。
8、基于损伤力学推导了钢纤维卵石混凝土和钢纤维再生混凝土弯曲疲劳损伤方程，结果显示，由疲劳损伤方程得到的回归曲线与疲劳损伤演化曲线吻合很好。
9、根据材料的宏观量的变化与疲劳损伤演变有本质联系，故由损伤变量推导得到钢纤维混凝土剩余疲劳寿命和剩余弯曲强度的表达式。通过该式，可求得给定疲劳应力水平、不同损伤状态下的剩余疲劳寿命和剩余弯曲强度，为有损结构的安全评估及决策提供参考。由剩余疲劳寿命随损伤变量以及循环比的变化曲线可知，随着损伤变量的增大，剩余疲劳寿命曲线下降，损伤变量为0.3以内时，剩余疲劳寿命降幅较大，且应力水平越低，降幅越明显，应力水平为0.7时，曲线急剧下降；随着循环比的增加，剩余疲劳寿命近似直线下降，且应力水平越低，降幅越明显。由剩余弯曲强度随循环比以及损伤变量的变化曲线可以看出，随循环比的不断增加，剩余弯曲强度逐渐降低，近似呈直线变化，当接近破坏时，剩余弯曲强度急剧下降，另外，循环比相同时，应力水平的变化对剩余弯曲强度的影响较小；而剩余弯曲疲劳强度随损伤变量近似呈直线变化，损伤变量相同时，应力水平越高，剩余弯曲强度越大。
Steel Fiber Reinforced Concrete (SFRC) is a new type of composite material made of adding randomly distributed short steel fibers to ordinary concrete. It has excellent properties of ordinary concrete, and steel fibers limit crack propagation, so brittle concrete in nature shows a high crack resistance and can delay the appearance of cracks, and SFRC has larger ductility and toughness and excellent tensile, flexural, impact, abrasion, anti-fatigue properties. In recent years, SFRC has been widely used and deeply studied. According to present research results at home and abroad, static and fatigue damage of SFRC has been studied in this paper, and the main researches and conclusions are as follows:
1. The method of how to convert the load-deflection curves of4-point bending beam obtained from tests into the corresponding stress-strain curves has been given. According to the energy equivalent prinple and the weibull statistical distribution theory, the constitutive model and the damage model of SFRC under single direction loading have been derived. As long as accurate determinations of the elastic modulus, the peak stress and peak strain of specimens were given, the constitutive equation and the damage evolution equation of SFRC under single direction loading could be derived.
2. The static failure can be seen as a special fatigue failure, which means the static failure is the fatigue failure only bearing one-cycle loading. Damage is also a process of gradual accumulation during loading. By learning from the analysis of fatigue damage, the damage evolution equation describing the relationship between the damage variable and strain under uniaxial loading could be derived based on the damage theory. According to the strain equivalence principle the corresponding constitutive equation could also be obtained.
3. Bending fatigue tests of steel fiber reinforced recycled concrete (SFRRC) and steel fiber reinforced pebble concrete (SFRPC) have been carried out. Fatigue lives at different stress levels (S=0.7,0.75,0.8,0.85) were obtained. Analysis results showed that the relationship between the stress level S and the logarithm of fatigue life N was linear, and the correlation coefficient was above0.99; fatigue life of SFRRC was greater than that of SFRPC at any stress level because of different interfacial bonding strength. The fatigue life equation obtained by summarizing present literature could be used to estimate fatigue life under flexural fatigue loading. Fatigue strain displayed the three-stage development law, and fatigue strain of SFRRC developed more slowly than that of SFRPC when increasing the cycle ratio. So it was obvious that SFRRC with the recycled aggregate as the coarse aggregate could not only change construction waste into resource treasure, reduce environmental pollution and realize resource recycling, but also show that its fatigue life and fatigue strain development were superior to those of SFRPC.
4. The Lognormal distribution and Weibull distribution were used to test fatigue lives of SFRRC and SFRPC. Results showed that the experimental fatigue lives could preferably obey Lognormal and two parameter Weibull distributions. Linear relationships of the single logarithm fatigue equation and the double logarithm fatigue equation under different survival ratios P and stress levels S were established, and the correlation coefficients were above0.99. Survival ratios P had little effect on the regression coeffients B and b of SFRPC, so average values of these two regression coeffients could be used as universal results. Survival ratios P had little effect on all regression coeffients of SFRRC, so average values could be used as universal results.
5. Through fitting the experimental fatigue data of SFRC with two gradings of aggregates, the fatigue equation was recommended, and the regression coefficient was above0.971. It was closer to the experimental fatigue data compared with other fitting equations.
6. The fatigue strain evolution equation was proposed to describe the fatigue strain evolution curves of SFRC, and the fitting curves had a good agreement with the experimental curves. It was observed that under constant amplitude fatigue loading, the fatigue modulus was inversely related to the fatigue strain, so by use of symmetry the fatigue modulus evolution equation was obtained according to the fatigue strain evolution equation. Present experimental data of fatigue modulus was used to test the suggested fatigue modulus evolution equation. It was found that the fitting curves expressed by the fatigue modulus evolution equation coincided with the experimental curves very well, and the correlation coefficients were all above0.99. So it showed that the suggested fatigue modulus evolution equation was appropriate for describing fatigue modulus evolution curves of SFRC.
7. The damage variable evolution curves obtained by use of the fatigue strain and fatigue modulus defining the damage variable showed that the damage variable evolution curves defined by the maximum fatigue strain and fatigue residual strain were basically consistent and the deviations were quite small, but the damage variable evolution curve defined by the fatigue modulus was significantly larger than that defined by the fatigue strain. When the cycle ratio was0.9, the damage variable value defined by the fatigue strain was about0.35, and the value defined by fatigue modulus was about0.77. When the initial cycle started, the damage variable value defined by the fatigue modulus was about0.34, but the value defined by the fatigue strain was close to0. That was to say, the damage variable value defined by the fatigue modulus was always larger than that defined by the fatigue strain.
8、Based on the damage mechanics, the flexural fatigue damage equation of SFRC was derived. Results showed that the fitting curves obtained by the suggested fatigue damage equation had a good agreement with the experimental fatigue evolution curves.
9、The residual fatigue life equation and residual flexural strength equation of SFRC were derived by the damage variable according to the essential relation between macroscopic quantity variation of materials and fatigue damage evolution. So the residual fatigue life and residual flexural strength could be got at given fatigue stress level and different damage conditions by these equations This could supply reference for safe estimate and decision on damage structure. It could be known from the relationships between the residual fatigue life and the damage variable and the cycle ratio, the residual fatigue life decreased in curve with increasing the damage variable; when the damage variable was within0.3, the decreasing range of the residual fatigue life was larger; and lower the stress level was, clearer was the decreasing range; when the stress level was0.7, the curve dropped sharply. The residual fatigue life decreased approximately in straight line with increasing the cycle ratio, smaller the stress level was, clearer was the decreasing range. It could be known from the relationships between the residual flexural strength and the damage variable and the cycle ratio, the residual flexural strength decreased approximately in straight line with increasing the cycle ratio; and the residual flexural strength descended sharply close to failure. In addition, variation of the stress level had little influence on the residual flexural strength at the same cycle ratio; the residual flexural strength varied approximately in straight line with the damage variable, and higher the stress level was, larger was the residual flexural strength.
1、给出了将试验得到的4点弯曲梁的荷载－挠度曲线转化为相应的应力－应变曲线的方法；根据能量等效原理和weibull统计分布理论推导了钢纤维混凝土在单向荷载作用下的本构模型及其损伤模型，只要能准确的测定出试件的弹性模量、峰值应力以及相应的峰值应变，就能得到其单向荷载作用下的本构方程和损伤演变方程。
2、静载破坏可看成是特殊的疲劳破坏，即极限强度加载下，承受一个循环的疲劳破坏。在此过程中，损伤也是一个逐步累积的过程。借鉴疲劳损伤的分析方法，基于损伤力学推导了单轴加载作用下描述损伤变量与应变关系的损伤演变方程。根据应变等效原理，得到对应的本构方程。
3、对钢纤维再生混凝土和钢纤维卵石混凝土弯曲疲劳性能进行了试验研究，得到不同应力水平（S=0.7,0.75,0.8,0.85）下的疲劳寿命。分析结果表明：应力水平S与对数疲劳寿命lgN成直线关系，相关系数在0.99以上，因钢纤维和粗骨料之间的界面连接强度不同，在任何应力水平下钢纤维再生混凝土的疲劳寿命都比钢纤维卵石混凝土大。综合已有文献回归得到的弯曲疲劳载荷作用下的疲劳寿命方程，可作为弯曲疲劳荷载作用下疲劳寿命的估算。钢纤维再生混凝土和钢纤维卵石混凝土弯曲疲劳应变演化曲线呈现三阶段发展规律，随着循环比的增加，钢纤维再生混凝土的疲劳应变比钢纤维卵石混凝土的疲劳应变发展慢。由此可见，利用再生骨料作为粗骨料的钢纤维再生混凝土不仅能“变废为宝”，减少环境污染，实现资源的重复利用，而且其疲劳寿命和疲劳应变发展都优于钢纤维卵石混凝土。
4、利用威布尔分布和对数正态分布对钢纤维再生混凝土和钢纤维卵石混凝土的疲劳寿命试验结果进行检验，结果表明本次试验的弯曲疲劳寿命较好地服从对数正态分布和两参数威布尔分布。不同存活率P和应力水平S下，单对数疲劳方程和双对数疲劳方程的线性关系是成立的，其相关系数R均在0.99以上；存活率P对钢纤维卵石混凝土的回归系数B和b影响很小，可取其平均值作为通用结果，而存活率P对钢纤维卵石混凝土各回归系数影响很小，可取其平均值作为通用结果。
5.通过对二级配钢纤维混凝土疲劳试验数据进行回归，提出了二级配钢纤维混凝土弯曲疲劳方程，其回归系数可以达到0.971以上，比采用其他拟合公式更接近试验结果。
6.提出了描述钢纤维混凝土的疲劳应变演化曲线的疲劳应变方程，结果显示，拟合曲线与试验曲线能很好吻合。根据疲劳模量与疲劳应变幅值成反比的关系，由疲劳应变演化方程得到疲劳模量演化方程。利用疲劳模量演化方程对已有疲劳模量试验结果进行拟合，结果显示，该式表达的疲劳模量演化曲线与相应的试验曲线吻合很好，其相关系数均在0.99以上，说明该式适合描述钢纤维混凝土的疲劳模量演化曲线。
7、分别用疲劳应变和疲劳模量定义钢纤维混凝土疲劳损伤，得到的典型的损伤变量演化曲线显示，由最大疲劳应变和疲劳残余应变定义的损伤变量演化曲线基本一致，且相差很小；而由疲劳模量定义的损伤变量演化曲线明显大于由疲劳应变定义的损伤变量演化曲线，当循环比为0.9时，由疲劳应变定义的损伤变量约0.35左右，而疲劳模量定义的损伤变量约为0.77，当初始循环时，疲劳模量定义的损伤变量就达到0.34左右，而疲劳应变定义的损伤变量接近0。也就是说，由疲劳模量定义的损伤变量自始至终都比疲劳应变定义的损伤变量大。
8、基于损伤力学推导了钢纤维卵石混凝土和钢纤维再生混凝土弯曲疲劳损伤方程，结果显示，由疲劳损伤方程得到的回归曲线与疲劳损伤演化曲线吻合很好。
9、根据材料的宏观量的变化与疲劳损伤演变有本质联系，故由损伤变量推导得到钢纤维混凝土剩余疲劳寿命和剩余弯曲强度的表达式。通过该式，可求得给定疲劳应力水平、不同损伤状态下的剩余疲劳寿命和剩余弯曲强度，为有损结构的安全评估及决策提供参考。由剩余疲劳寿命随损伤变量以及循环比的变化曲线可知，随着损伤变量的增大，剩余疲劳寿命曲线下降，损伤变量为0.3以内时，剩余疲劳寿命降幅较大，且应力水平越低，降幅越明显，应力水平为0.7时，曲线急剧下降；随着循环比的增加，剩余疲劳寿命近似直线下降，且应力水平越低，降幅越明显。由剩余弯曲强度随循环比以及损伤变量的变化曲线可以看出，随循环比的不断增加，剩余弯曲强度逐渐降低，近似呈直线变化，当接近破坏时，剩余弯曲强度急剧下降，另外，循环比相同时，应力水平的变化对剩余弯曲强度的影响较小；而剩余弯曲疲劳强度随损伤变量近似呈直线变化，损伤变量相同时，应力水平越高，剩余弯曲强度越大。
Steel Fiber Reinforced Concrete (SFRC) is a new type of composite material made of adding randomly distributed short steel fibers to ordinary concrete. It has excellent properties of ordinary concrete, and steel fibers limit crack propagation, so brittle concrete in nature shows a high crack resistance and can delay the appearance of cracks, and SFRC has larger ductility and toughness and excellent tensile, flexural, impact, abrasion, anti-fatigue properties. In recent years, SFRC has been widely used and deeply studied. According to present research results at home and abroad, static and fatigue damage of SFRC has been studied in this paper, and the main researches and conclusions are as follows:
1. The method of how to convert the load-deflection curves of4-point bending beam obtained from tests into the corresponding stress-strain curves has been given. According to the energy equivalent prinple and the weibull statistical distribution theory, the constitutive model and the damage model of SFRC under single direction loading have been derived. As long as accurate determinations of the elastic modulus, the peak stress and peak strain of specimens were given, the constitutive equation and the damage evolution equation of SFRC under single direction loading could be derived.
2. The static failure can be seen as a special fatigue failure, which means the static failure is the fatigue failure only bearing one-cycle loading. Damage is also a process of gradual accumulation during loading. By learning from the analysis of fatigue damage, the damage evolution equation describing the relationship between the damage variable and strain under uniaxial loading could be derived based on the damage theory. According to the strain equivalence principle the corresponding constitutive equation could also be obtained.
3. Bending fatigue tests of steel fiber reinforced recycled concrete (SFRRC) and steel fiber reinforced pebble concrete (SFRPC) have been carried out. Fatigue lives at different stress levels (S=0.7,0.75,0.8,0.85) were obtained. Analysis results showed that the relationship between the stress level S and the logarithm of fatigue life N was linear, and the correlation coefficient was above0.99; fatigue life of SFRRC was greater than that of SFRPC at any stress level because of different interfacial bonding strength. The fatigue life equation obtained by summarizing present literature could be used to estimate fatigue life under flexural fatigue loading. Fatigue strain displayed the three-stage development law, and fatigue strain of SFRRC developed more slowly than that of SFRPC when increasing the cycle ratio. So it was obvious that SFRRC with the recycled aggregate as the coarse aggregate could not only change construction waste into resource treasure, reduce environmental pollution and realize resource recycling, but also show that its fatigue life and fatigue strain development were superior to those of SFRPC.
4. The Lognormal distribution and Weibull distribution were used to test fatigue lives of SFRRC and SFRPC. Results showed that the experimental fatigue lives could preferably obey Lognormal and two parameter Weibull distributions. Linear relationships of the single logarithm fatigue equation and the double logarithm fatigue equation under different survival ratios P and stress levels S were established, and the correlation coefficients were above0.99. Survival ratios P had little effect on the regression coeffients B and b of SFRPC, so average values of these two regression coeffients could be used as universal results. Survival ratios P had little effect on all regression coeffients of SFRRC, so average values could be used as universal results.
5. Through fitting the experimental fatigue data of SFRC with two gradings of aggregates, the fatigue equation was recommended, and the regression coefficient was above0.971. It was closer to the experimental fatigue data compared with other fitting equations.
6. The fatigue strain evolution equation was proposed to describe the fatigue strain evolution curves of SFRC, and the fitting curves had a good agreement with the experimental curves. It was observed that under constant amplitude fatigue loading, the fatigue modulus was inversely related to the fatigue strain, so by use of symmetry the fatigue modulus evolution equation was obtained according to the fatigue strain evolution equation. Present experimental data of fatigue modulus was used to test the suggested fatigue modulus evolution equation. It was found that the fitting curves expressed by the fatigue modulus evolution equation coincided with the experimental curves very well, and the correlation coefficients were all above0.99. So it showed that the suggested fatigue modulus evolution equation was appropriate for describing fatigue modulus evolution curves of SFRC.
7. The damage variable evolution curves obtained by use of the fatigue strain and fatigue modulus defining the damage variable showed that the damage variable evolution curves defined by the maximum fatigue strain and fatigue residual strain were basically consistent and the deviations were quite small, but the damage variable evolution curve defined by the fatigue modulus was significantly larger than that defined by the fatigue strain. When the cycle ratio was0.9, the damage variable value defined by the fatigue strain was about0.35, and the value defined by fatigue modulus was about0.77. When the initial cycle started, the damage variable value defined by the fatigue modulus was about0.34, but the value defined by the fatigue strain was close to0. That was to say, the damage variable value defined by the fatigue modulus was always larger than that defined by the fatigue strain.
8、Based on the damage mechanics, the flexural fatigue damage equation of SFRC was derived. Results showed that the fitting curves obtained by the suggested fatigue damage equation had a good agreement with the experimental fatigue evolution curves.
9、The residual fatigue life equation and residual flexural strength equation of SFRC were derived by the damage variable according to the essential relation between macroscopic quantity variation of materials and fatigue damage evolution. So the residual fatigue life and residual flexural strength could be got at given fatigue stress level and different damage conditions by these equations This could supply reference for safe estimate and decision on damage structure. It could be known from the relationships between the residual fatigue life and the damage variable and the cycle ratio, the residual fatigue life decreased in curve with increasing the damage variable; when the damage variable was within0.3, the decreasing range of the residual fatigue life was larger; and lower the stress level was, clearer was the decreasing range; when the stress level was0.7, the curve dropped sharply. The residual fatigue life decreased approximately in straight line with increasing the cycle ratio, smaller the stress level was, clearer was the decreasing range. It could be known from the relationships between the residual flexural strength and the damage variable and the cycle ratio, the residual flexural strength decreased approximately in straight line with increasing the cycle ratio; and the residual flexural strength descended sharply close to failure. In addition, variation of the stress level had little influence on the residual flexural strength at the same cycle ratio; the residual flexural strength varied approximately in straight line with the damage variable, and higher the stress level was, larger was the residual flexural strength.
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