Non-linear earthquake response of concrete gravity dams part 1: Modelling

A finite element procedure to model the non-linear earthquake response of concrete gravity dam systems is presented. A two-dimensional idealization is adopted for the dam and water in order to simplify the analysis and reduce the computational effort. The foundation of the dam is modelled as a rigid rectangular massless plate attached to a three-dimensional viscoelastic half-space. The non-linear behaviour is represented by smearing techniques and includes tensile cracking with subsequent opening, closing and sliding, as well as water cavitation in the reservoir. Special treatments are applied to suppress spurious oscillations in the water response associated with cavitation and to prevent cracks in the dam from spreading into wide zones. Experience from non-linear analyses is cited as it affects the design of the algorithm.     

Non-linear seismic response of arch dams

An experimental study of non-linear mechanisms that may occur during intense seismic response of arch dams is described in this paper. The presentation deals with three types of non-linearity that were observed during shaking table model studies: monolith joint opening, cantilever cracking, and reservoir cavitation at the dam face. The monolith joint opening phenomenon was represented by a segmental arch ring model that simulated a horizontal slice of a prototype dam. The cantilever cracking and reservoir cavitation mechanisms were studied using a model gravity dam section. The principal conclusion of the investigation was that shaking table experiments provide a practical means of studying the non-linear earthquake response of concrete arch dams, including their actual failure mechanisms.     

Effects of concrete cracking on the earthquake response of gravity dams

Tensile stresses exceeding the tensile strength of concrete can develop in concrete dams subjected to earthquake ground motion. This study examines the earthquake response of gravity dams including tensile cracking of the concrete. The interaction between the dam and compressible water is included in the analysis using a numerical procedure for computing the non-linear dynamic response of fluid-structure systems. The crack band theory is used to model tensile cracking with modifications to allow for the large finite elements necessary for dam analysis. The earthquake response of a typical gravity dam monolith shows that concrete cracking is an important non-linear phenomenon. Cracking is concentrated near the base of the dam and near the discontinuities in the face slope. The extensive cracking, which develops due to ground motion typical of maximum credible earthquakes, may affect the stability of dams during and after strong earthquakes.     

Integrative seismic safety evaluation of a high concrete arch dam

An integrative seismic safety evaluation of an arch dam should include all sources of nonlinearities, dynamic interactions between different components and the external loads. The present paper investigates the calibration procedure and nonlinear seismic response of an existing high arch dam. The first part explains the conducted analyses for the static and thermal calibrations of the dam based on site measurements. The second part investigates the nonlinear seismic analysis of the calibrated model considering the effect of joints, cracking of mass concrete, reservoir–dam–rock interaction, hydrodynamic pressure inside the opened joints and the geometric nonlinearity. Penetration of the water inside the opened joints accelerates the damage process. The integrative seismic assessment of a case study shows that the dam will fail under the maximum credible earthquake scenario. The dam is judged to be severely damaged with extensive cracking and the joints undergo opening/sliding. A systematic procedure is proposed for seismic and post-seismic safety of dams.     

APPLICATION OF BOUNDARY ELEMENT ANALYSIS FOR MULTIPLE SEISMIC CRACKING IN CONCRETE GRAVITY DAMS

The previously developed two-dimensional boundary element procedure for analysing the propagation of a single discrete crack is extended to simultaneous multiple cracking in concrete gravity dams. A brief discussion of the generalized methodology is presented and the validity of the extended procedure is verified by performing a fracture analysis of the Fongman dam and comparing the predicted rupture process with the available experimental results. The fracture response of the Koyna dam is then studied extensively under the Koyna earthquake. Both single and multiple cracking models are employed to investigate the fracture process as well as final rupture in the dam. Similar final damage involving complete separation of the crest block of the dam is predicted, irrespective of whether single or multiple crack propagation models are employed. In relation to the phenomenon of hydrodynamic uplift pressure within propagating cracks, openings of the crack on the upstream face of the dam are examined in particular. The results indicate that this phenomenon is not expected to be significant during the crack development phase, and hence unlikely to affect the final rupture characteristics of dams undergoing strong earthquake excitation.     

考虑劣化屈服老化裂纹后混凝土水库堤坝排水边坡抗震性研究

针对在水库堤坝排水边坡混凝土裂纹的抗震性研究中,未考虑岩土体抗剪强度参数的劣化屈服效应以及混凝土裂纹的老化,存在抗震性判断结果准确率较差等问题,提出水库堤坝排水边坡混凝土考虑老化后产生裂纹的抗震性能研究方法。模拟强震下边坡混凝土的开裂破坏过程,根据D-P屈服准则,实现对闸墩混凝土材料的屈服判断。采用薄层整体单元模拟和分离式裂纹单元,实现混凝土裂纹的数值模拟,加载地震波后,获取混凝土裂纹的强震响应规律与破坏特征。实验结果可知,本文方法对坝体位移变化的研究精度高,得到的混凝土裂纹扩展范围更为准。运用本文方法对水库堤坝排水边坡混凝土的抗震性研究准确率以及可信度较高,说明本文方法具有一定的可取性。     

Seismic failure modeling of concrete dams considering heterogeneity of concrete

Study on the failure process of high concrete dams subjected to strong earthquakes is crucial to reasonable evaluation of their seismic safety. Numerical simulation in this aspect involves dynamic failure analysis of big bulk concrete dam subjected to cyclic loading. The Rock Failure Process Analysis (RFPA) proposed by C.A. Tang, with successful applications to failure modeling of rock and concrete specimens mainly subjected to static loading, is extended for this purpose. For using the proposed model, no knowledge on the cracking route needs to be known beforehand, and no remeshing is required. Simulation of the whole process of elastic deformation, initiation and propagation of microcracks, severe damage and ultimate failure of concrete dams in earthquakes with a unified model is enabled. The model is verified through a shaking table test of an arch dam. Finally a practical gravity dam is employed as a numerical example. Considering the uncertainty in ground motion input and concrete material, typical failure process and failure modes of gravity dam are presented. Several small cracks may occur due to tension particularly at dam neck, dam faces and dam heel, and a few of them evolve into dominant ones. Relatively smaller earthquake may cause damage to the dam neck while a bigger one may bring on cracks at lower parts of the dams. Cracking at the dam bottom may incline to a direction almost perpendicular to the downstream face after propagating horizontally for a certain distance when the shaking is strong enough.     

Seismic failure modeling of concrete dams considering heterogeneity of concrete

Study on the failure process of high concrete dams subjected to strong earthquakes is crucial to reasonable evaluation of their seismic safety. Numerical simulation in this aspect involves dynamic failure analysis of big bulk concrete dam subjected to cyclic loading. The Rock Failure Process Analysis (RFPA) proposed by C.A. Tang, with successful applications to failure modeling of rock and concrete specimens mainly subjected to static loading, is extended for this purpose. For using the proposed model, no knowledge on the cracking route needs to be known beforehand, and no remeshing is required. Simulation of the whole process of elastic deformation, initiation and propagation of microcracks, severe damage and ultimate failure of concrete dams in earthquakes with a unified model is enabled. The model is verified through a shaking table test of an arch dam. Finally a practical gravity dam is employed as a numerical example. Considering the uncertainty in ground motion input and concrete material, typical failure process and failure modes of gravity dam are presented. Several small cracks may occur due to tension particularly at dam neck, dam faces and dam heel, and a few of them evolve into dominant ones. Relatively smaller earthquake may cause damage to the dam neck while a bigger one may bring on cracks at lower parts of the dams. Cracking at the dam bottom may incline to a direction almost perpendicular to the downstream face after propagating horizontally for a certain distance when the shaking is strong enough.     

Numerical simulation of reinforcement strengthening for high‐arch dams to resist strong earthquakes

This paper focuses on analyzing the nonlinear seismic response of high‐arch dams with cantilever reinforcement strengthening. A modified embedded‐steel model is presented to evaluate the effects of the strengthening measure on alleviating the extension and opening of cracks under strong earthquakes. By stiffening reinforced steel, this model can easily consider the steel–concrete interaction for lightly reinforced concrete (RC) members without the need of dividing them into RC and plain concrete zones. The new tensile constitutive relations of reinforced steel are derived from the load–deformation relationship of RC members in direct tension. This model has been implemented in the finite element code and its applicability is verified by two numerical simulations for RC tests. Subsequently, numerical analyses for a 210‐m high‐arch dam (Dagangshan arch dam) are conducted with and without the presence of cantilever reinforcement. Numerical results show that reinforcement strengthening can reduce the nonlinear response of the arch dam, e.g. joint opening and crest displacement, and limit the extension and opening width of concrete cracks. Copyright © 2008 John Wiley & Sons, Ltd.     

Earthquake analysis of concrete gravity dams including dam-water-foundation rock interaction

A general procedure for analysis of the response of concrete gravity dams, including the dynamic effects of impounded water and flexible foundation rock, to the transverse (horizontal) and vertical components of earthquake ground motion is presented. The problem is reduced to one in two dimensions, considering the transverse vibration of a monolith of the dam. The system is analysed under the assumption of linear behaviour for the concrete, foundation rock and water. The complete system is considered as composed of three substructures—the dam, represented as a finite element system, the fluid domain, as a continuum of infinite length in the upstream direction, and the foundation rock region as a viscoelastic half-plane. The structural displacements of the dam are expressed as a linear combination of Ritz vectors, chosen as normal modes of an associated undamped dam-rock system. The effectiveness of this analytical formulation lies in its being able to produce excellent results by considering only a few Ritz vectors. The generalized displacements due to earthquake motion are computed by synthesizing their complex frequency responses using Fast Fourier Transform procedures. The stress responses are calculated from the displacements. An example analysis is presented to illustrate results obtained from this analytical procedure. Computation times for several analyses are presented to illustrate the effectiveness of the procedure.     

Efficient non-linear seismic analysis of arch dams

An approximate procedure for seismic analysis of concrete arch dams which is based on the smeared crack method is described. Features include construction sequence modelling, water and foundation interaction, crack formation, opening and closing of joints and cracks, frictional sliding, presence of shear keys, action of internal water pressure, and a reliable solution algorithm. Complete solutions can be obtained in an hour on a fast workstation computer, allowing parameter studies to be run. Results suggest that an arch dam can suffer significant cracking during strong ground shaking and still remain stable. © 1998 John Wiley & Sons, Ltd.     

A unified approach for long-term behavior and seismic response of AAR-affected concrete dams

Concrete dams suffering from alkali-aggregate reaction (AAR) exhibit swelling and deterioration of concrete or even cracking over a long period. The deterioration of concrete may significantly affect the dynamic behavior of the structures, and it is necessary to estimate seismic safety of the deteriorated dams subjected to strong earthquakes. A unified approach is presented in this paper for long-term behavior and seismic response analysis of AAR-affected concrete dams by combining AAR kinetics, effects of creep and plastic-damage model in the finite element method. The proposed method is applied to a gravity dam and an arch dam. The long-term behavior of the AAR-affected dams is first predicted in terms of anisotropic swelling, spatially non-uniform deterioration of concrete, and cracking initiation and propagation with the development of AAR. The seismic response of the deteriorated dams is subsequently analyzed based on the state of the structures at the end of the long-term analysis. The AAR-induced expansion displacements obtained from the proposed method are in good agreement with the measured ones in the long-term operation. The simulated cracking patterns in the dams caused by the continuing AAR are also similar to the field observation. The results from the seismic analysis show that AAR-induced deterioration of concrete and cracking may lead to more severe damage cracking in the dams during earthquake. The dynamic displacements are also increased compared with the dams that are not suffering from AAR. The seismic safety of the AAR-affected concrete dams is significantly reduced because of the AAR-induced deterioration of concrete and cracking.     

Shaking table test on small‐scale retrofitted model of Sefid‐rud concrete buttress dam

Sefid‐rud concrete buttress dam with a height of 106 m was damaged during the devastating 1990 Manjil earthquake. The dam was repaired and strengthened using epoxy grouting of cracks and the installation of post‐tensioned anchors. In a previous study, nonlinear seismic response of the highest monolith with empty reservoir was investigated experimentally through model testing. A geometric‐scaled model of 1:30 was tested on a shaking table to study dynamic cracking of the model. As a result of the similarity between model and prototype cracking pattern, the model was retrofitted according to prototype retrofitting plan after the Manjil earthquake and re‐tested on shaking table to estimate the current safety of the prototype. Experimental test results showed that the post‐tensioning resulted in a significant decrease in dynamic responses in terms of crest displacement and measured strains of the retrofitted model in comparison with its corresponding responses at the first test. No cracking was observed in the retrofitted model when the base motion peak acceleration exceeded a value that was 22% higher than the one caused cracking in the first model. This can be interpreted as the efficiency of prototype post‐tensioning system in evaluating the seismic safety of Sefid‐rud dam. Copyright © 2009 John Wiley & Sons, Ltd.     

考虑流固耦合效应的辽宁葠窝水库溢流坝段抗震性能分析

针对辽宁葠窝水库混凝土重力坝抗震问题,采用耦合的拉格朗日-欧拉有限元分析技术,建立了可考虑库水-坝体-基岩动力耦合效应的典型溢流坝段抗震分析数值模型。模型中,采用等效一致粘弹性边界模拟基岩的人工截断边界;采用混凝土弥散裂缝本构模型模拟混凝土的动力特性。根据烈度与地震动之间的关系,确定了水库坝体抗震设计的输入加速度峰值。据此,分析了在不同季节水位变化条件下坝体地震反应的基本特性。研究表明：完好的辽宁葠窝水库混凝土重力坝溢流坝段能满足8度的抗震设防烈度要求。地震下溢流坝段峰值位移出现在胖坝和瘦坝的坝顶迎水面位置处,胖坝的动位移较瘦坝动位移大。胖坝在闸墩与溢流堰交接处出现了拉应力最大值。有库水条件下,瘦坝峰值拉应力出现在坝趾处,无库水条件下,瘦坝最大拉应力出现在溢流堰与闸墩交接处。     

Direct finite element method for nonlinear analysis of semi‐unbounded dam–water–foundation rock systems

A direct finite element method is presented for nonlinear earthquake analysis of interacting dam–water–foundation rock systems. The analysis procedure applies viscous damper absorbing boundaries to truncate the semi‐unbounded fluid and foundation‐rock domains and specifies at these boundaries effective earthquake forces determined from the design ground motion defined at a control point on the free surface. The analysis procedure is validated numerically by computing the frequency response functions and transient response of an idealized dam–water–foundation rock system and comparing with results from the substructure method. Because the analysis procedure is applicable to nonlinear systems, it allows for modeling of concrete cracking, as well as sliding and separation at construction joints, lift joints, and at concrete–rock interfaces. Implementation of the procedure is facilitated by commercial finite element software with nonlinear material models that permit modeling of viscous damper boundaries and specification of effective earthquake forces at these boundaries. Copyright © 2017 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.     

Linear and nonlinear response of concrete slab on CFR dam during earthquake

The joint between concrete slab and rockfill is designed as welded contact in the classical modeling of concrete-faced rockfill (CFR) dams and earthquake response of the CFR dams is determined by this method. In this study, linear and nonlinear response of Torul CFR Dam including interface element between concrete slab and rockfill were investigated for the duration of strong seismic excitation. The finite element analyses were performed by employing both cases, empty and full reservoir, to research the effect of the reservoir water on the earthquake response of the dam. The reservoir water was modeled with fluid finite elements by the Lagrangian approach. The Drucker-Prager model was used in nonlinear analyses for concrete slab, rockfill and soil materials. According to finite element analyses, displacement and stress components were increased by hydrodynamic pressure. The nonlinear response of the concrete slab was monitored about the peak ground acceleration (pga). This study reveals that the size of sliding zone increases with increasing acceleration amplitudes.     

Nonlinear dynamic response of concrete gravity dams: cavitation effect

A finite element method for the dynamic analysis of concrete gravity dams is presented. Displacement based formulation is used for both fluid and structural domains. During severe ground motion, the impounding fluid in the reservoir may separate from the dam and cause forming of micro bubbles. As a result, the compressibility of water is reduced. This nonlinear phenomenon of the reservoir is termed cavitation. When the direction of the ground motion is changed, the micro bubble's region of fluid collapses, and an impact will occur. By using different damping ratios in the fluid and solid domains the spurious oscillations which were caused by the impact are removed. The cavitation is confined to the upper part of the reservoir, where it has an effect of paramount importance on the tensile stresses. To illustrate the cavitation effect, the response of the non-overflow monolith of the Pine Flat dam subjected to the first 6.5 s of the May 1940 El-Centro, California earthquake, is considered. In order that the cavitation phenomenon take place more widely, maximum acceleration was scaled to give an amplitude of 1 g.     

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.     

Effects of reservoir bottom absorption and dam-water-foundation rock interaction on frequency response functions for concrete gravity dams

The linear response of an idealized concrete gravity dam monolith to harmonic horizontal or vertical ground motion is presented for a range of the important system parameters that characterize the properties of the dam, foundation rock, impounded water and reservoir bottom materials. Based on these frequency response functions, the effects of alluvium and sediments at the reservoir bottom on the response of the dam, including its interaction with the impounded water and foundation rock, are investigated. It is shown that the partial absorption of hydrodynamic pressure waves by the reservoir bottom materials has an important effect on the dynamic response of concrete gravity dams.