混凝土相关外文翻译.doc

温州大学本科毕业设计 建筑与土木工程学院Application of thermodynamics-based rate-dependent constitutive models of concrete in the seismic analysis of concrete damsAbstract: This paper discusses the seismic analysis of concrete dams with consideration of material nonlinearity. Based on a consistent rate-dependent model and two thermodynamics-based models, two thermodynamics-based rate-dependent constitutive models were developed with consideration of the influence of the strain rate. They can describe the dynamic behavior of concrete and be applied to nonlinear seismic analysis of concrete dams taking into account the rate sensitivity of concrete. With the two models, a nonlinear analysis of the seismic response of the Koyna Gravity Dam and the Dagangshan Arch Dam was conducted. The results were compared with those of a linear elastic model and two rate-independent thermodynamics-based constitutive models, and the influences of constitutive models and strain rate on the seismic response of concrete dams were discussed. It can be concluded from the analysis that, during seismic response, the tensile stress is the control stress in the design and seismic safety evaluation of concrete dams. In different models, the plastic strain and plastic strain rate of concrete dams show a similar distribution. When the influence of the strain rate is considered, the maximum plastic strain and plastic strain rate decrease.Key words: concrete; constitutive model; rate dependency; concrete dam; nonlinearity; seismic analysis1 IntroductionChina has abundant water resources. As part of the national energy and water conservancy plan, a batch of 300 m-level high concrete arch dams are or will soon be under construction. Most of the dams are situated in regions of strong seismic activity. Their designed seismic accelerations reach 0.2g-0.32g ( g = 9.81 m/s2 ), with a probability of exceedance of 2% over a 100-year period. The designed maximum acceleration of the Dagangshan Arch Dam even reaches 0.5575g. The influence of earthquakes should be considered and cautious arguments and investigations should be made about the seismic safety of the dams to ensure their safe operation and minimize damage from earthquakes. Great progress has been made in the field of technology for dynamic analysis of concrete dams during earthquakes. However, some issues need to be better understood, including the nonlinear constitutive model and dynamic behavior of concrete, which are still based on elastic analysis (Lin and Chen 2001; IWHR 1997). A rational constitutive model of concrete is the foundation of further research on thenonlinear behavior of concrete. An appropriate constitutive model can reflect the mechanical characteristics of the material in all the stages of deformation, including strain hardening and softening, strength reduction, and stiffness degradation, which determine the progressive damage of concrete. After several decades of development, the plastic theory describes these characteristics of concrete with a rather good theoretical basis. Nevertheless, there are too many hypotheses in the present plastic and viscoplastic models of concrete, including the Drucker postulate, associated or non-associated flow rules, and plastic potential functions, some of which have no clear physical significance and others of which do not conform to the thermodynamic laws (Leng et al. 2008). For the nonlinear analysis of concrete dams, it has become important to construct a constitutive model with few hypotheses, which can conform to the energy principle and reflect the nonlinear behavior of concrete. In the meantime, concrete is a typical rate-sensitive material, whose strength, stiffness and ductility (or brittleness) are subject to a loading speed. Obviously, considerable deviation would be caused by the static mechanical parameters for seismic analysis. Identifying material characteristics of concrete under different strain rates and establishing proper dynamic constitutive models of concrete have become prerequisites for nonlinear dynamic analysis of arch dams. The descriptions of dynamic behavior of concrete in the Specifications for Seismic Design of Hydraulic Structures (IWHR 1997) are very simple and need further supplement and improvement. Based on a consistent viscoplastic model, two thermodynamics-based consistent rate-dependent models were derived from two thermodynamics-based static models with consideration of the influence of the strain rate. They satisfy thermodynamic laws automatically and can authentically describe the dynamic behavior of concrete. With the two models, the seismic responses of the Koyna Gravity Dam and the Dagangshan Arch Dam were analyzed. The nonlinear dynamic behavior of concrete dams and the influence of the strain rate on the dynamic behavior of concrete dams were discussed through comparison with the linear elastic model and the rate-independent models.2 Introduction to thermodynamics-based rate-dependentconstitutive models of concreteOn the basis of the classical plastic theory, a consistent rate-dependent model takes into consideration the influence of the strain rate and maintains that stress remains on the yield surface in viscoplastic flow (Wang 1997). Therefore, the consistency condition is satisfied. The yield criteria with the strain rate effect can be expressed generally as （1）where is the stress tensor, is an internal variable, is the rate of the internal variable, and is the viscoplastic multiplier.Due to the rarity of multiaxial dynamic experiments of concrete at present, the multiaxialdynamic constitutive relationship cannot be established directly. It is assumed for simplicitys sake that the dynamic increase factor (DIF) of multiaxial strength is the same as that of uniaxial strength.Concrete shows completely different behavior under tension and under compression.Therefore, the internal variable is split into two parts, and , and behaviors under tension and under compression are described separately by means of these two internal variables. Under uniaxial compressive or tensile loading, we have , （2） and in a complex stress state, we have ， （3） where and are the weighting functions of compressive and tensile internal variables, respectively. The principles for determining and are as follows: for the loading process with dominant tensile stress states, =1 and =0 ; similarly, for the loading process with dominant compressive stress states, =0 and =1; for other loading conditions, 01, 0 1 , and + =1. Finally, the yield criterion can be expressed as ； (4) According to the theory of the consistent rate-dependent model, a consistency condition should be satisfied: ： (5) Two thermodynamics-based plastic constitutive models of concrete that have simple forms and can satisfy the energy laws naturally have been developed by Leng et al. (2008). Results from both models, obtained under static loading, agree with experimental results. The two models have been established, respectively, in Haigh-Westergaard stress space and principle stress space, the difference being that the Lode angle is neglected in the Haigh-Westergaard stress space model and considered in the principle stress space model. The two yield criteria can be expressed as (6)and (7)where p is the volumetric stress; q is the shear stress; and are the shift stresses on the hydrostatic axis and principle stress axis, respectively; , , and are the stress dimensions, where i=(1,2,3,); and are the intersection points of the yield surface and hydrostatic axis; and , , ，and are dimensionless parameters to be determinedThe plastic flow rules of the two models are, respectively, (8)and (9)where ；, the relative level of shift stress; and are the volumetric plastic strain increment and deviatoric plastic strain increment, respectively; ; ; and , and are three principle plastic strain increments.According to the results of experiments (Suaris and Shah 1985; Reinhardt 1984), the relationships between the compressive and tensile strengths of concrete and the internal variable and rate of the internal variable are （10）and （11）where and are dynamic strengths of concrete under uniaxial compression and tension, respectively, and , , and are assumed functions that can be obtained from experimental data.The internal variable is considered the equivalent plastic strain: (12)where is the viscoplastic strain increment, and m is the unit tensor of plastic flow, which is determined by Eq. (8) or Eq. (9).Substituting these equations into the consistency condition leaves us with (13)where The consistent viscoplastic model can be solved with an implicit backward Euleralgorithm, which has been studied and modified by Winnicki et al. (2001), Carosio et al. (2000) and Montans (2000).The thermodynamic approach not only achieves greater generality, but also offers significant theoretical insights. In thermodynamics-based models, fewer hypotheses are made about the form of the dissipation function, and no assumptions are made about the plastic potential functions and flow rule. Benefitting from appropriate hardening and softening functions and relationships between the strength, modulus and strain rate, thermodynamics-based rate-dependent models reasonably describe the behavior of concrete under static and dynamic loading (Leng et al. 2008).以热力学为基础的频率依赖性混凝土本构模型在混凝土坝于地震作用中分析的应用摘要：本文论述了大坝在地震中考虑材料性能的非线性分析。根据连续性模，两个基于热力学的频率依赖性混凝土本构模型在考虑了应变率影响完善后的应用。这两个模型可以描述混凝土的动态性能。并且适用于混凝土坝在考虑了其材料的敏感性后在地震作用中的非线性分析。运用这两个模型可以对重力坝和大岗山拱坝在地震中进行非线性分析。本文对于混凝土坝动态性能中的混凝土坝非线性动力响应和应变率对其的影响这两个因素是通过比较线弹性模型和非频率依赖性这两个模型进行讨论的。从分析中可以得出：在混凝土抗震安全评估中，抗拉应力是控制应力。混凝土坝的塑性应变和应变率分布曲线在不同的模型中有着相似的分布情况。当考虑了应变率的影响，最大塑性应变和应变率将会有所降低。关键词：混凝土；本构模型；频率依赖性；混凝土坝；非线性；抗震分析1前言中国有丰富的水资源。作为国家水利规划的一部分，一批300M级高强度的混凝土的拱坝很快会被建设起来。大多数大坝位于强震地区。他们的设计地震加速度是以100年内达到0.2g0.3g（g=9.81m/）超过2%为概率设计的。大岗山拱坝的设计最大地震加速度甚至达到0.5575g。设计应该考虑地震的影响，精准的调查应该以大坝在地震中的安全状态为论据，以确保大坝的安全和减少大坝受地震的影响。目前，在混凝土坝在地震中的动态分析技术领域已取得重大的突破。然而，基于混凝土弹性分析的非线性模型动态分析的具体问题仍需进一步探索（Lin and Chen 2001;IWHR1997）。合理的混凝土本构模型是建立在进一步研究混凝土的非线性基础上。一个适当的结构模型可以反映机械的特殊性材料在所有阶段的变形，包括收缩和徐变、强度、刚度的降低，从而进一步确定混凝土的破坏状况。经过了几十年的发展，阐述混凝土特性的塑性理论已具有相当好的理论基础。然而，目前的塑性和弹塑性混凝土也有许多假设没有明确的物理意义或不符合热力学定律的，其中包括德鲁克假设、相关或非相关流动法则和塑性势函数(Leng et al.2008)。混凝土坝的非线性分析，可以用很少的假设建立结构模型，况且符合能量守恒和反应混凝土的非线性。同时，混凝土是一种典型的应变率敏感材料，其强度、刚度和塑性（或脆性）受加载速度影响明显。显然，用静态力学参数进行地震作用分析会引起很大的误差。标识混凝土在不同应变率下特点，建立合理的动态混凝土本构模型已经成为拱坝非线性动态分析的先决条件。抗震规范中的混凝土动态性能分析描述运用到水利结构设计（IWHR 1997）是不够的，需要进一步的补充与改进。根据连续粘塑性模型，两个基于热力学的连续频率依赖性模型是由考虑了应变率的影响的两个基于热力学静态模型派生而来的。他们满足热力学定律且能真实的反应混凝土的动态性能。用这两种模型就能对重力坝和大岗山拱坝的地震作用进行分析。对于混凝土坝动态性能中的混凝土坝非线性动力响应和应变率对其的影响这两个因素是通过比较线弹性模型和非频率依赖性这两个模型进行讨论的。2混凝土结构模型热力学原理的相关说明 以经典塑性理论为基础，连续频