Seismic cracking and energy dissipation in concrete gravity dams

A finite element method for seismic fracture analysis of concrete gravity dams is presented. The proposed smeared crack analysis model is based on the non-linear fracture behaviour of concrete. The following features have been considered in the development of the model: (i) the strain softening of concrete due to microcracking; (ii) the rotation of the fracture band with the progressive evolution of microcrack damage in finite elements; (iii) the conservation of fracture energy; (iv) the strain-rate sensitivity of concrete fracture parameters; (v) the softening initiation criterion under biaxial loading conditions; (vi) the closing-reopening of cracks under cyclic loading conditions. The seismic fracture and energy response of dams and the significance of viscous damping models to take account of non-cracking structural energy dissipation mechanisms are discussed. The influences of global or local degradation of the material fracture resistance on the seismic cracking response of concrete dams were also studied. Two-dimensional seismic response analyses of Koyna Dam were performed to demonstrate the application of the proposed non-linear fracture mechanics model.     

A RATE-DEPENDENT ISOTROPIC DAMAGE MODEL FOR THE SEISMIC ANALYSIS OF CONCRETE DAMS

In this paper a rate-dependent isotropic damage model developed for the numerical analysis of concrete dams subjected to seismic excitation is presented. The model is shown to incorporate two features essential for seismic analysis: stiffness degradation and stiffness recovery upon load reversals and strain-rate sensitivity. The issue of mesh objectivity is addressed using the concept of the ‘characteristic length’ of the fracture zone, to show that both the softening modulus and the fluidity parameter must depend on it to provide consistent results as the computational mesh is refined. Some aspects of the numerical implementation of the model are also treated, to show that the model can be easily incorporated in any standard non-linear finite element code. The application of the proposed model to the seismic analysis of a large gravity concrete dam shows that the structural response may vary significantly in terms of the development of damage. The inclusion of rate sensitivity is able to reproduce the experimental observation that the tensile peak strength of concrete can be increased up to 50 percent for the range of strain rates that appear in a structural safety analysis of a dam subjected to severe seismic actions.     

具有割缝的大理岩试件破坏过程的有限元模拟

本文使用应变软化的弹塑性本构模型,用有限元方法对具有中心斜割缝的岩石试件在轴压下的破坏过程进行了数值模拟。得到了与实验观察相当一致的结果:在割线端部附近,首先发生张破裂,裂纹的扩张是逐渐地弯向试件的轴线方向,并变为稳定的。随着轴向压力增加,在张裂纹的相反方向上出现共轭的剪破裂。这些现象与割缝顶端附近材料的应变软化性质有关。说明所采用的有限元方法是研究岩石材料破裂过程的一种可行的方法。     

A continuum damage concrete model for earthquake analysis of concrete gravity dam–reservoir systems

In this study, the earthquake damage response of the concrete gravity dams is investigated with considering the effects of dam–reservoir interaction. A continuum damage model which is a second-order tensor and includes the strain softening behavior is selected for the concrete material. The mesh-dependent hardening technique is adopted such that the fracture energy dissipated is not affected by the finite element mesh size. The dynamic equilibrium equations of motion are solved by using the improved form of the HHT-α time integration algorithm. Two dimensional seismic analysis of Koyna gravity dam is performed by using the 1967 Koyna earthquake records. The effects of damage on the earthquake response of concrete gravity dams are discussed. Comparison of the Westergaard and Lagrangian dam–reservoir interaction solutions is made. The effects of viscous damping ratio on the damage response of the dam are also studied.     

An application of damage mechanics for seismic analysis of concrete gravity dams

This paper discusses the local approach of fracture using damage mechanics concepts to evaluate the seismic response of concrete gravity dams. A constitutive model for plain concrete, subjected to tensile stresses, is presented. The mesh-dependent hardening technique is adopted such that the fracture energy dissipated is not affected by the finite element mesh size. The model is implemented in conjunction with the Hilber, Hughes Taylor alpha algorithm for time marching. Koyna dam is utilized to validate the proposed formulation. The importance of initial damage prior to the advent of an earthquake is also investigated. A 60 m concrete gravity dam is therefore selected and subjected to ground motion typical of eastern North America. Five scenarios of initial damage are presented and the results confirm the importance of accounting for the initial state for the seismic safety evaluation of an existing dam.     

A thermo-plastic constitutive law for brittle-plastic behavior of rocks at high temperatures

Mechanical properties of rocks change under the influence of, temperature. Stress at the onset of yielding, ultimate strength, dilatancy, strain hardening and softening, and the confining pressure at brittle-ductile transition are all reduced by the increasing temperature. This study presents a framework of constitutive modeling of thermo-brittle-plastic behavior of rocks which encompasses these changes. The constitutive law is based on a thermo-plasticity theory first proposed for metals byPrager (1958). Two phenomenological mechanisms have been identified as central for the modeling: temperature dependence of the yield locus (thermal softening), and temperature dependence of the strain-hardening function (thermally enhanced ductility). Material parameters for two rocks, Carrara marble and Westerly granite, were determined on the basis of additional hypotheses. These parameters are used in numerical simulations of triaxial tests at different temperatures. The obtained stress-strain curves compare well to the experimental results. The changes with temperature in the stress at the onset of yielding are more accurately reproduced that the evolution of hardening or softening. Suggestions for possible improvements and future research directions are indicated.     

The stiffness degradation and damping ratio evolution of Taipei Silty Clay under cyclic straining

The non-linear behavior of Taipei Silty Clay under cyclic strain loading was investigated through a series of undrained cyclic strain-controlled tests. The Ramberg–Osgood equation was used with our proposed stiffness degradation model to calculate degraded secant moduli. The proposed degradation model is simple in that it has only one more component than Idriss's model, the modulus ratio for the first cycle, which reflects the effects of the previous cyclic strain history and the current level of the cyclic strain amplitude, and can be used to describe softening and hardening behavior under irregular cyclic straining. It was found that the Ramberg–Osgood equation successfully predicts the damping ratio for small to medium strains. However, it overestimates the damping ratio for larger strains, so we suggest it can be corrected with a damping ratio index. In addition, the proposed equation for describing the evolution of the damping ratio provides the means to assess the variation for Taipei Silty Clay in the measured damping ratio with both the number of cycles and the strain amplitude.     

大理岩试件中裂缝的逆向共轭剪破裂

本文介绍了以激光全息干涉法观测单轴压缩下,大理岩岩样表面的变形位移场。全息干涉图可以反映出由于岩石内部微裂隙丛集激增所导致的变形局部化,实验采用板状大理岩试件,在中心处预制了不同角度的裂缝,实验在MTS伺服压机中加载直至宏观破坏,观测了裂隙的发展过程。实验表明:当裂缝角小于45时,先在裂缝尖端处的张应力集中部位出现新裂纹,它的起裂角(与原裂缝的交角)90,裂纹弯向压力方向并趋于稳定。当>45时,在上述张裂纹稳定后,在裂缝尖端附近再次发生张裂,其起裂角60,同样弯向压力方向后稳定。在这些前期张破裂稳定后,在张裂的相反方向,也即裂缝的共轭方向上,出现内部微裂隙的丛集,并随后发生宏观的剪破坏,我们认为此逆向剪切破坏与大理岩的多晶组构有关,与应变弱化过程中变形和应力的调整有关。      

A plastic-damage concrete model for earthquake analysis of dams

A new plastic-damage constitutive model for cyclic loading of concrete has been developed for the earthquake analysis of concrete dams. The rate-independent model consistently includes the effects of strain softening, represented by separate damage variables for tension and compression. A simple scalar degradation model simulates the effects of damage on the elastic stiffness and the recovery of stiffness after cracks close. To simulate large crack opening displacements, the evolution of inelastic strain is stopped beyond a critical value for the tensile damage variable. Subsequent deformation can be recovered upon crack closing. The rate-independent plastic-damage model forms the backbone model for a rate-dependent viscoplastic extension. The rate-dependent regularization is necessary to obtain a unique and mesh objective numerical solution. Damping is represented as a linear viscoelastic behaviour proportional to the elastic stiffness including the degradation damage. The plastic-damage constitutive model is used to evaluate the response of Koyna dam in the 1967 Koyna earthquake. The analysis shows two localized cracks forming and then joining at the change in geometry of the upper part of the dam. The upper portion of the dam vibrates essentially as rigid-body rocking motion after the upper cracks form, but the dam remains stable. The vertical component of ground motion influences the post-cracking response. © 1998 John Wiley & Sons, Ltd.     

The effects of strong motion duration on the dynamic response and accumulated damage of concrete gravity dams

Strong motion duration is one of the challenging characteristics of ground motion, which affects the cumulative damage of structures significantly. Many researchers have conducted investigations related to the effects of strong motion duration on the response of building structures. However, the corresponding studies of concrete gravity dams are limited. In this paper, the effects of strong motion duration on the accumulated damage of concrete gravity dams are investigated. A Concrete Damaged Plasticity (CDP) model including the strain hardening or softening behavior is selected for the concrete material. This model is used to evaluate the nonlinear dynamic response and seismic damage process of Koyna dam during 1976 Koyna earthquake. Subsequently, the damage analyses of Koyna dam subjected to earthquake motions with different strong motion durations are performed. 20 as-recorded accelerograms, which are modified to match a 5% damped target spectrum, are considered in this study. Strong motion durations are obtained based on the definition of significant duration. According to the characteristics of the cracking damage development, both local and global damage indices are established as the response parameters. The results show that strong motion duration is positively correlated to the accumulated damage for events with similar response spectrum, and has significant influence on the cumulative damage of the dam. Longer duration will lead to greater accumulation damage to which aseismic design of the dam should be given attention.     

应变率效应对600 MPa级高强钢筋混凝土框架结构抗震性能影响研究

为了更真实地进行钢筋混凝土结构抗震性能评估,应该考虑材料的应变率效应影响。600 MPa级高强钢筋作为新一代建筑钢材,尚无考虑应变率效应影响的600 MPa级高强钢筋混凝土框架结构抗震性能研究。首先进行了不同应变率下600 MPa级高强钢筋拉伸力学性能试验,利用试验数据拟合得到600 MPa级高强钢筋在不同应变率下的强度提高系数表达式,并利用OpenSees软件进行了配置600 MPa级高强钢筋混凝土框架结构抗震性能模拟分析,研究了应变率效应对框架结构抗震性能的影响。研究结果表明:随着应变率的增大,钢筋的屈服强度和极限强度均得到提高,屈服强度最大提高11.5%,极限强度最大提高8.9%;随着所考虑的材料应变率增加,配置600 MPa级高强钢筋框架结构最大顶点位移总体上呈减小趋势,地震波强度越强,应变率效应影响越大,而层间位移角减小幅值相差不大。研究成果可作为600MPa级高强钢筋混凝土框架结构抗震评估的依据。     

岩石塑性变形条件下的Mohr-Coulomb屈服准则

传统的Mohr-Coulomb强度准则仅描述了峰值强度状态下正应力和剪应力之间的关系,作为岩石破坏的判据.本文拓展概念,提出Mohr-Coulomb屈服准则表述岩石发生塑性变形后不同应力状态下屈服面的应力应变关系.在总结实验研究的基础上建立了使用三轴压缩试验数据确定塑性参数c和φ随内变量κ变化的实验技术方法,给出了评价各向同性模型精度的参量表达以及某些测试结果.采用具有各向同性强(软)化规律的Mohr-Coulomb屈服准则,利用岩石的初始屈服、峰值屈服和残余屈服三组参数可以将全过程应力应变曲线简化表征为四直线模型,它比三线性模型有更广泛的适用性.本文的结果为工程地质数值模拟提供了理论和实验基础,具有指导意义.     

闭合裂纹面相互作用的实验研究

为了研究地震过程中断层面的相互作用,设计了四类裂纹面状况不同的断裂力学实验。实验结果表明,裂纹面的状况对于含裂纹材料的σ_c(2^1/2)值有强烈的影响,并利用断裂力学的原理对结果进行了分析。 实验中解决了如下技术关键: 1.可用三点弯曲、局部受拉、单面启裂、双面贯穿的方法,在脆性材料板状试件（玻璃板、岩石板）以及有机玻璃板中预制中心穿透裂纹。 2.在裂纹端部预计裂纹扩展的区域内粘贴电阻应变片,用以判断并测量裂纹初始扩展及其相应的破坏应力σ_c的方法。     

Modelling of material non-linearities in steel structures subjected to transient dynamic loading

This paper is concerned with the modelling of the behaviour of steel under cyclic and dynamic loading conditions. After a general discussion regarding the requirements for accurate and efficient modelling in dynamics, two models are described and implemented. The bilinear stress-strain constitutive relationship with kinematic hardening is widely used in many computer codes, hence is used for ‘control’ purposes. The multisurface plasticity model is said to exhibit the important qualities of strain hardening, softening and relaxation to a mean stress. This model is described in detail and notes on model parameter evaluation are given. A number of validation examples are presented, due to the complexity of implementation of the multisurface formulation. This is followed by comparisons between the bilinear response predictions and those of the multisurface model for cyclic and dynamic tests on beam-columns. It is concluded that in the absence of material test data under cyclic loading, the bilinear model provides acceptably accurate response predictions. However, the multisurface model provides a significantly closer fit to experimental results, due to its ability to model a yield plateau and a non-linear strain-hardening regime as well as cyclic degradation. It can also be used for new types of steel where no distinct yield point is observed.     

基于能量耗散原理的非均质岩石损伤破坏元胞自动机模型研究

基于能量耗散理论建立非均质岩石的动态损伤破坏元胞自动机,分析单轴压缩试验中岩石破坏截面的损伤状态,得到该情况下的岩石裂隙微观动态发展过程、损伤演化关系以及全程应力应变曲线。研究发现：①加载过程中,均质度较低的岩样裂纹的萌生和扩展较为分散,损伤速率低;均质度较高的岩样裂纹的萌生和扩展非常集中,表现为脆性破坏。②损伤演化曲线呈3阶段S形发展。③随着岩石均质度参数的增加,岩石的峰值强度和峰值应变都有所提高,峰后曲线越来越陡。④给出的衡量岩石脆性破坏强弱程度的指标参数,能够较好地描述岩石破坏形式随着均值度参数m变化的规律。     

A damage model for structures with degrading response

The paper presents a hysteretic damage model for the response simulation of structural components with strength and stiffness deterioration under cyclic loading. The model is based on 1D continuum damage mechanics and relates any 2 work‐conjugate response variables such as force‐displacement, moment‐rotation, or stress‐strain. The strength and stiffness deterioration is described by a continuous damage variable. The formulation uses a criterion based on the hysteretic energy and the maximum or minimum deformation for damage initiation with a cumulative probability distribution function for the damage evolution. A series of structural component response simulations showcase the ability of the model to describe different types of hysteretic behavior. The relation of the model's damage variable to the Park‐Ang damage index is also discussed. Because of its consistent and numerically robust formulation, the model is suitable for the large‐scale seismic response simulation of structural systems with strength and stiffness deterioration.     

红层泥岩填料的力学特性及本构模型研究

在红层泥岩地区进行道路工程施工时,考虑到材料短缺和成本问题,常常采用就地取材的方式作为路基填料。为了研究红层泥岩填料的适用性,选取甘肃省永登县某工点的风化红层泥岩填料为研究对象,在室内开展一系列三轴CU剪切试验,探究含水率、围压和压实度对应力-应变曲线、峰值(残余)强度、抗剪强度指标的影响,并对不同类型的应力-应变曲线,分别采用相应的模型进行拟合。研究结果表明：含水率、围压和压实度对其物理力学特性具有显著影响;对符合应变软化型规律的曲线,采用沈珠江的双曲线模型拟合的规律一般;对符合应变硬化型规律的曲线,采用Duncan-Chang模型拟合的规律较好。研究结果可以为甘肃省红层泥岩路基的病害处治与维修提供参考依据。