基于热力学原理的混凝土本构模型及其在大坝地震分析中的应用
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摘要
本文构造了混凝土在塑性过程中的能量耗散增量函数形式,推导了基于热力学原理的混凝土弹塑性本构模型,并将之推广得到了率型一致粘塑性模型。模型能自动满足热力学定律,具有较为严密的理论基础,与试验结果符合良好。最后利用本文模型对Koyna重力坝和大岗山拱坝进行动力非线性地震反应分析,探讨了各模型以及应变率对大坝地震反应的影响。
论文介绍了基于热力学原理建立本构模型的基本理论和一般过程,以能量耗散函数为基础讨论了耗散应力空间的屈服函数;尝试从宏观角度和细微角度分析了部分塑性功恢复的机理;从理论上证明了混凝土流动法则的相关性和非正交性;根据Ziegler正交假定确定了耗散应力空间的流动法则;通过迁移应力确定了真实应力空间中的屈服函数和流动法则,建立了完整的本构模型。
修改Collins提出的耗散函数,构造了适用于混凝土的耗散函数,推导了混凝土材料的本构模型。根据部分模型参数的物理意义和屈服面的几何形状,确定了部分模型参数的取值范围。根据已有的试验资料,拟合了模型参数,计算结果与试验符合较好,验证了模型的正确性和有效性。
构造了一个主应力空间中耗散增量函数以描述混凝土材料屈服函数在π平面上非圆形的轨迹。得到的模型能够反映混凝土材料对静水压力的敏感性以及拉压不等性,能够较好地描述出非正交的塑性流动和混凝土在单轴受压下的体积膨胀。拟合参数后,计算得到的单双轴拉压曲线与试验吻合情况良好,对比显示计算效果更好。
根据一致率型粘塑性模型的概念,在基于能量耗散的混凝土静态模型中引入应变率的影响,建立了基于热力学的一致率型粘塑性模型,并与试验结果进行了比较,结果表明模型能够较好地反映混凝土试件的动力特性,同时计算混凝土结构的动力反应,考虑应变率的影响后,结构的响应发生了较大的变化,因此,应变率对混凝土结构响应的影响是一个不可忽视的因素。
用线弹性模型和本文率无关、率相关共五个模型计算了Koyna重力坝和大岗山拱坝的地震反应,并初步探讨了不同模型以及应变率对大坝地震反应的影响,计算结果表明拉应力成为大坝震设计中的控制应力。考虑应变率对混凝土性能的影响后,混凝土的抗拉强度得到提高,坝体能承受的拉应力提高,拉坏区缩小,塑性应变也有所减小,塑性应变率也发生明显变化。相比受拉,应变率对坝体中压应力的分布没有明显影响。本文的计算结果为大岗山拱坝的设计和抗震安全评价提供了参考。
In the dissertation, a form of energy dissipation fuction in the plastic procedure of concrete is constructed, and thermodynamics-based elasto-plastic constitutive models of concrete are derived and generalized to rate-dependent consistent visco-plastic model. The models have strict theoretical basis and automatically satisfy the thermodynamic laws. The performance of models coincides with experiments. Finally nonlinear seismic responses of Koyna gravity dam and Dagangshan arch dam are analyzed, and the effects of models and strain rate are discussed.
The fundamental theories and general procedure of establishing constitutive models based on thermodynamic laws are introduced. Proper energy dissipation function is studied and the yield function in dissipation stress space is deduced. The mechanism of recoverable plastic work is tried to be analyzed macroscopically and mesoscopically. The association and non-normality of plastic flow of concrete are proved. The flow rule in dissipation stress space is determined in terms of Ziegler orthogonality principle. The yield function and the flow rule in true stress space are deduced by the shift stress with the above procedures performed, a complete constitutive model is established.
An incremental function of energy dissipation in principle stress is constructed to describe the non-circle loci of concrete yield function inπplane. The sensitivity to hydrostatic pressure and the unequal behavior of concrete subjected to tension and compression loading can be represented by the model. The non-normal plastic flow and the dilatancy of concrete under uniaxial compression are also well described. The stress-strain curves of concrete under uniaxial and biaxial tension and compression with parameters fitted are in good agreement with experiments.
Based on the concept of consistent viscoplasticity constitutive model, consistent rate-dependent viscoplastic models are constructed with the effects of strain rate considered in the static models based on energy dissipation. Compared with experiments, the consistent rate-dependent viscoplastic models can well represent dynamic behavior of concrete specimens. The responses of concrete structures are calculated, the results show that the responses of concrete structures vary apparently with the effects of strain rate considered. Therefore, the influence of strain rate is inneglectable in the analysis of concrete structures.
Seismic responses of Koyna gravity dam and Dagnagshan arch dam are analyzed with linear elastic model, rate-independent models and rate-dependent models presented respectvely, and the influence of different models and strain rate on seismic responses are discussed. It shows that tensile stress is the control stresses of seismic design of arch dam. With the influence of strain rate considered, the strength of concrete is enhanced, and the dam can sustain higher tensile stress, so the plastic strain decreases and the region of failure shrinks, and the plastic strain rate changes as well. Compared with tensile stress, compressive stress is not influenced much by strain rate. The calculations provide reference for seismic design and safety evaluation of Dagangshan arch dam.
论文介绍了基于热力学原理建立本构模型的基本理论和一般过程,以能量耗散函数为基础讨论了耗散应力空间的屈服函数;尝试从宏观角度和细微角度分析了部分塑性功恢复的机理;从理论上证明了混凝土流动法则的相关性和非正交性;根据Ziegler正交假定确定了耗散应力空间的流动法则;通过迁移应力确定了真实应力空间中的屈服函数和流动法则,建立了完整的本构模型。
修改Collins提出的耗散函数,构造了适用于混凝土的耗散函数,推导了混凝土材料的本构模型。根据部分模型参数的物理意义和屈服面的几何形状,确定了部分模型参数的取值范围。根据已有的试验资料,拟合了模型参数,计算结果与试验符合较好,验证了模型的正确性和有效性。
构造了一个主应力空间中耗散增量函数以描述混凝土材料屈服函数在π平面上非圆形的轨迹。得到的模型能够反映混凝土材料对静水压力的敏感性以及拉压不等性,能够较好地描述出非正交的塑性流动和混凝土在单轴受压下的体积膨胀。拟合参数后,计算得到的单双轴拉压曲线与试验吻合情况良好,对比显示计算效果更好。
根据一致率型粘塑性模型的概念,在基于能量耗散的混凝土静态模型中引入应变率的影响,建立了基于热力学的一致率型粘塑性模型,并与试验结果进行了比较,结果表明模型能够较好地反映混凝土试件的动力特性,同时计算混凝土结构的动力反应,考虑应变率的影响后,结构的响应发生了较大的变化,因此,应变率对混凝土结构响应的影响是一个不可忽视的因素。
用线弹性模型和本文率无关、率相关共五个模型计算了Koyna重力坝和大岗山拱坝的地震反应,并初步探讨了不同模型以及应变率对大坝地震反应的影响,计算结果表明拉应力成为大坝震设计中的控制应力。考虑应变率对混凝土性能的影响后,混凝土的抗拉强度得到提高,坝体能承受的拉应力提高,拉坏区缩小,塑性应变也有所减小,塑性应变率也发生明显变化。相比受拉,应变率对坝体中压应力的分布没有明显影响。本文的计算结果为大岗山拱坝的设计和抗震安全评价提供了参考。
In the dissertation, a form of energy dissipation fuction in the plastic procedure of concrete is constructed, and thermodynamics-based elasto-plastic constitutive models of concrete are derived and generalized to rate-dependent consistent visco-plastic model. The models have strict theoretical basis and automatically satisfy the thermodynamic laws. The performance of models coincides with experiments. Finally nonlinear seismic responses of Koyna gravity dam and Dagangshan arch dam are analyzed, and the effects of models and strain rate are discussed.
The fundamental theories and general procedure of establishing constitutive models based on thermodynamic laws are introduced. Proper energy dissipation function is studied and the yield function in dissipation stress space is deduced. The mechanism of recoverable plastic work is tried to be analyzed macroscopically and mesoscopically. The association and non-normality of plastic flow of concrete are proved. The flow rule in dissipation stress space is determined in terms of Ziegler orthogonality principle. The yield function and the flow rule in true stress space are deduced by the shift stress with the above procedures performed, a complete constitutive model is established.
An incremental function of energy dissipation in principle stress is constructed to describe the non-circle loci of concrete yield function inπplane. The sensitivity to hydrostatic pressure and the unequal behavior of concrete subjected to tension and compression loading can be represented by the model. The non-normal plastic flow and the dilatancy of concrete under uniaxial compression are also well described. The stress-strain curves of concrete under uniaxial and biaxial tension and compression with parameters fitted are in good agreement with experiments.
Based on the concept of consistent viscoplasticity constitutive model, consistent rate-dependent viscoplastic models are constructed with the effects of strain rate considered in the static models based on energy dissipation. Compared with experiments, the consistent rate-dependent viscoplastic models can well represent dynamic behavior of concrete specimens. The responses of concrete structures are calculated, the results show that the responses of concrete structures vary apparently with the effects of strain rate considered. Therefore, the influence of strain rate is inneglectable in the analysis of concrete structures.
Seismic responses of Koyna gravity dam and Dagnagshan arch dam are analyzed with linear elastic model, rate-independent models and rate-dependent models presented respectvely, and the influence of different models and strain rate on seismic responses are discussed. It shows that tensile stress is the control stresses of seismic design of arch dam. With the influence of strain rate considered, the strength of concrete is enhanced, and the dam can sustain higher tensile stress, so the plastic strain decreases and the region of failure shrinks, and the plastic strain rate changes as well. Compared with tensile stress, compressive stress is not influenced much by strain rate. The calculations provide reference for seismic design and safety evaluation of Dagangshan arch dam.
引文
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