This paper provides a complete probabilistic analysis method and a performance-based seismic safety evaluation for high concrete faced rockfill dam (CFRD). Combined with random sample generation and reliability analysis methods, the dynamic response characteristics and reliability level of CFRD under various random factors are comprehensively described. In Chapter 2, a random ground motion model based on spectral representation-random function and a high-dimensional random variable generation method based on GF-discrepancy are established. Combined with probability density evolution method (PDEM) and the random sample generation methods to verify its effectiveness and reliability for nonlinear complex geotechnical engineering. In Chapter 3, the dynamic response and probabilistic characteristics of high CFRD under random ground motion are revealed based on the elastoplastic analysis. A performance-based seismic safety evaluation method is established. In Chapter 4, the influence of material parameter randomness on dynamic response and seismic safety of high CFRD is studied from the perspective of stochastic dynamics and probability. In Chapter 5, the stochastic dynamic response and probability distribution of high CFRD under the coupled random action of ground motion and material parameters are systematically studied, and the performance-based seismic safety evaluation framework is improved. In Chapter 6, The stochastic dynamic response of 3D high CFRD is studied, and the failure performance index and performance level based on overstress volume ratio combined with overstress accumulation time are discussed. The performance-based seismic safety evaluation framework is further improved. In Chapter 7, combined with the finite element dynamic time-history analysis method considering the softening effect of rockfill, a performance-based seismic safety evaluation framework for dam slope stability of high CFRD under multiple random factors is systematically explored from the perspective of stochastic dynamics and probability. In Chapter 8, The performance indexes of seismic safety evaluation for high CFRDs are suggested and the corresponding performance level with probability assurance is put forward. The multi-seismic intensity—multi-performance target—failure probability performance relationship is established, and a performance-based seismic safety evaluation framework is initially formed. This book can be used as a reference for scholars studying random vibration and reliability analysis, as well as for scholars studying dam safety evaluation.
1.1 Background
Although the western region of China is rich in hydropower resources and is suitable for the construction of large hydro projects. These projects are in the Himalayan-Mediterranean seismic belt and the geological conditions are relatively complex, the seismic intensity is high (Fig. 1.1), and the seismic activity is relatively frequent (Fig. 1.2). According to the statistics of China Earthquake Administration, more than 80% of the strong earthquakes in modern times occurred in the western region of China. Since the twentieth century, there have been nearly 70 severe earthquakes with a magnitude of more than 7 (Zhang 2017), among which the most typical are the Wenchuan earthquake in Sichuan Province in 2008 and the Yushu earthquake in 2010. The results of seismic activity and earthquake trend prediction in China show that there may be about 40 earthquakes of magnitude 7 and above and 3–4 earthquakes of magnitude 8 and above in the mainland of China in the next hundred years (Kong and Zou 2016).
A map of China with a heatmap indcating seismic activity. The intensity is in the medium range from central to west along with many small patches of the highest intensity.
Fig. 1.1
Division map of seismic intensity in China
A map of China. It presents the distribution of earthquakes with magnitudes greater than 4.0. The region along the west and the central have the highest number of clustered spots. There are scattered spots in the rest of the entire region.
Fig. 1.2
Distribution of earthquakes with magnitudes greater than 4.0 in the last five years
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Therefore, under the threat of strong earthquakes, the safety of these high dams and reservoirs must be considered as a key issue in engineering construction. So far, there are few cases of earthquake-tested concrete faced rockfill dams and related earthquake damage. Only a few concrete faced rockfill dams over 50 m in the world have been subjected to strong earthquakes. For example: the Zipingpu Dam in China (Chen et al. 2008a, b; Chen et al. 2008a, b; Guan 2009a, b; Kong et al. 2011; Kong et al. 2011; Liu et al. 2015; Ren et al. 2016; Wang et al. 2018; Yang et al. 2009; Zhang et al. 2015; Zhao et al. 2009), the Cogoti Dam in Chile (Han and Kong 1996; Noguera 1987), the Minase Dam in Japan (Han and Kong 1996), the Malpasse Dam in Peru (Han and Kong 1996), the Cogswell Dam in the United States (Boulanger et al. 1995), and the Urto Kyisk Dam (Shen 2007a, b). The main earthquake damage forms are summarized as Table 1.1 (Zhang 2017). It can be seen that the main seismic damage of concrete faced rockfill dam is as follows: the dam body has settlement and displacement to the downstream direction; local cracking, damage, void and joint dislocation of the panel; the downstream dam slope rock rolls down and develops into shallow slope sliding. In the Wenchuan earthquake, the typical failure mode of the Zipingpu concrete faced rockfill dam is shown in Fig. 1.3. However, it is obvious from the earthquake damage cases that most of them only exhibited light and repairable local damage without dam break.
Table 1.1
Summary of earthquake damage situation in several CFRDs
Engineering
Year of completion
Height/m
Original time of earthquake
Earthquake magnitude
Damage condition
Cogoti Dam
1938
85
1943
8.3
Loose rocks on the crest and downstream dam slope become dislodged or even roll down. The downstream dam slope gradient changes from 1:1.5 (pre-earthquake) to 1:1.65 (post-earthquake). The dam crest experiences a settlement deformation of about 38.1 cm. Panels near the dam crest become suspended due to the settlement, leading to vertical cracks and crushing at the upper part of the panels. Opening of the surrounding joints results in vortex flow
Minase Dam
1963
66.5
1964
7.5
The dam body exhibits a horizontal displacement of 4 cm and a settlement of 6.1 cm. Cracks appear on the dam crest road surface, and there is slight damage to the panel joints with minor loss of integrity. The seepage rate increases from 90 L/s before the earthquake to 220 L/s after the earthquake
Zipingpu Dam
2006
156
2008
8.0
The maximum settlement of the dam reaches 0.81 m, which is notably significant. The downstream side of the dam experiences a horizontal displacement of over 0.3 m. Loose rock on the downstream face of the dam near the dam crest becomes dislodged and shifts. The panels show signs of compression damage, construction joint displacement, and partial detachment between the panels and the cushion layer, with a maximum offset of 17 cm. Seepage rate shows a slight increase compared to before the earthquake
A set of 4 photographs of damages during an earthquake. Top left, dam crest settlement. Top right, panel misalignment with phase 3 panel over the phase 2 panel. Bottom left, compressive failure with crumbling and peeling-off of plastering in a building wall. Bottom right, block stone sliding.
Fig. 1.3
The typical damage phenomenon of Zipingpu CFRD in Wenchuan earthquake
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It has shown that the dam designed and constructed in accordance with the current specification requirements has an appropriate degree of seismic capacity under earthquake action. However, as a complex natural disaster, the occurrence time, scene and intensity of earthquakes are full of randomness. The existing earthquake damage cases show that the real intensity of the dam site during the earthquake may far exceed the design intensity. For example, during the Wenchuan earthquake, the seismic intensity of the 150-m-level Zipingpu concrete faced rockfill dam was higher than its design intensity (the fortification intensity of the Zipingpu concrete faced rockfill dam project was VIII degrees. The design standard of 2% exceed probability in the base period of 100 years was adopted, and the peak acceleration of the design ground motion was 0.26 g. In the Wenchuan earthquake, the Zipingpu Water Conservancy Project is only 17.17 km away from the epicenter, and the seismic transmission intensity reaches IX–X degrees. The peak acceleration of the dam bedrock is greater than 0.5 g (Guan 2009a, b). More importantly, there is no high dam with a height of more than 200 m that has been tested by strong earthquakes, which can provide reference for seismic design and research up to now. Considering the irreplaceable important position of high dams in China, the seismic safety problems that cannot be ignored and the unpredictable secondary disasters, it is extremely important to ensure the seismic safety of high dams. Therefore, it is of great scientific significance and engineering value to study the seismic performance of high concrete faced rockfill dam under earthquake, especially under strong earthquake.
At present, the performance-based structural seismic safety design and safety evaluation methods have been widely studied in the fields of structural engineering, bridge engineering and other fields at home and abroad. However, in the field of high dams, especially high concrete faced rockfill dams, it is still in its infancy. From the analysis of the seismic performance level of the concrete faced rockfill dam, it illustrated that the randomness of the seismic load and the uncertainty of the structure itself may lead to different degrees of damage to the concrete face rockfill dam (Kartal et al. 2010; Wang et al. 2013), which will have an impact on the use function and engineering safety. Therefore, it is urgent to consider various uncertain factors under seismic action based on a variety of strong nonlinear analysis. At the same time, a reasonable evaluation method based on multi-performance indicators and different performance levels is proposed to gradually realize the transformation from deterministic analysis to uncertain probabilistic analysis. The purpose of this book is to consider the uncertainty of seismic load and structural material parameters, aiming for studying the failure probability of high concrete faced rockfill dam under earthquake by using strong nonlinear numerical analysis method. A performance-based seismic safety evaluation framework for high concrete faced rockfill dam is preliminarily established.
1.2 Performance-Based Research of Safety Evaluation of Dams
Considering the randomness and uncertainty of the seismic load and the dam structure itself, the dynamic response and failure of the dam are also random and uncertain in nature. When the earthquake occurs, the degree of structural damage caused by different probability levels is different. This will have an impact on the use function of the project and the cost of repair, and will also lead to different estimated costs and economic losses. Therefore, the analysis methods of safety assessment and failure process of high dams subjected to different intensity earthquakes need a further development. An index system which can be linked to the functional objectives of high dam seismic resistance and can express the seismic safety of high dam is constructed gradually. Finally, the unification of economy and security can be realized. According to the different materials, the dam is mainly divided into two types: concrete dam and earth-rock dam, which will show different seismic response characteristics. Zhang et al. (2016) carried out a systematic study on the theoretic of seismic design of high concrete dams. The basic framework of high dam seismic performance design based on seismic hazard analysis, dam seismic vulnerability analysis and seismic loss analysis is established.
1.2.1 Concrete Dam
Chen (2005) and Lin and Chen (2001) carried out the research work on the seismic safety evaluation, seismic fortification level and corresponding performance indexes of concrete dams. Based on the design service life and the function of the high dam, Jia and Jin (2005, 2006) proposed two methods related to the decision-making of high dam fortification standard, and pointed out that the minimum total expected loss was taken as the standard for the decision-making of optimal seismic fortification intensity. Shen (2007a, b) and Kou (2009) established a quantitative evaluation model for earthquake damage, and constructed a performance-based seismic safety and risk assessment system for high dams. Zhang et al. (2013) proposed a strategy for probabilistic analysis of the stochastic response of gravity dams based on the probabilistic analysis of dynamic response parameters of the dams. They obtained the probability distribution characteristics and patterns of gravity dams, and reasonably assessed the probabilities of various types of damage to gravity dams during earthquakes. Xu et al. (2010) constructed a model for probabilistic analysis of damage distribution in concrete gravity dams based on stochastic perturbation theory and virtual excitation method. They also developed an evaluation method for dam failure losses based on grey system dynamics. Yao et al. (2013) conducted research on seismic vulnerability analysis in the dynamic design of high arch dams and developed a performance-based seismic safety assessment method for high arch dams. Li et al. (2013) established an earthquake risk assessment approach for concrete gravity dams based on seismic hazard analysis, existing dam vulnerability analysis, and loss estimation. Li et al. (2012) utilized various artificial intelligence algorithms to construct vulnerability and risk analysis methods for concrete gravity dams. Pan et al. (2015) and Chen et al. (2019) introduced Incremental Dynamic Analysis (IDA) to perform seismic performance analysis on gravity dams and arch dams, offering a new approach for performance-based seismic design of dams, which achieved positive outcomes. Abroad, many scholars employed Incremental Dynamic Analysis and vulnerability analysis methods to analyze the seismic performance of concrete dams, exploring quantified standards for failure modes, gradually becoming a hot topic in the research of performance-based seismic safety assessment for dams, exhibiting strong novelty and practicality (Hariri et al. 2016; Hariri and Saouma 2016a; Hariri and Saouma 2016b; Hebbouche 2013; Kadkhodayan et al. 2016; Morales et al. 2016; Soysal et al. 2016; Tekie and Ellingwood 2003; Tekie 2002).
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1.2.2 Rockfill Dam
Currently, both domestically and internationally, there is limited research on performance-based seismic safety assessment of earth-rock dams, particularly high-profile concrete faced rockfill dams. Apart from conducting ultimate seismic capacity analysis (Chen et al. 2013; Lu and Dou 2014; Tian et al. 2013; Wang and Zhu 2017; Zhang and Li 2014; Zhao et al. 2015; Zhu et al. 2018), the research has mainly focused on assessing seismic safety from a probabilistic or vulnerability perspective, with some incorporation of seismic risk analysis. Wang et al. (2013, 2012) based on seismic risk analysis theory, established the evaluation indicators for relative settlement at the crest of the dam, divided the seismic damage levels of earth-rock dams, obtained risk probabilities for different damage levels through vulnerability analysis, and finally integrated seismic economic loss analysis to establish a method for seismic risk analysis of earth-rock dams. Wang et al. (2016) established vulnerability models for common failure modes (slope stability and permanent deformation) of high earth-rock dams under seismic loads, proposed a performance-based seismic risk analysis model and evaluation matrix for high earth-rock dams. Kartal et al. (2010), using the example of the Torul panel rockfill dam, employed an improved response surface method, considering uncertainties in material and geometric properties of panels and rockfill material, to analyze the crack resistance and compressive reliability of panels with different thicknesses under seismic effects. Wu et al. (2015) proposed a reliability analysis algorithm based on the generalized coordinate system, primarily used for analyzing seismic stability of dam slopes in high earth-rock dams.
From the above studies, it can be observed that for dam structures, performance-based seismic safety assessment primarily involves the analysis of various uncertain factors under seismic actions, as well as seismic response and probabilistic analysis. On the other hand, performance-based seismic safety assessment should be capable of anticipating a structure's seismic performance under potential future seismic actions. Seismic safety assessment should encompass three key points: seismic input motion, structural seismic response, and structural resistance. Therefore, "performance-based seismic safety assessment" can be summarized as ensuring that structures meet relevant seismic performance objectives under different specified seismic design levels. Its essence mainly includes: graded design standards, corresponding seismic design levels with performance objectives, and rational selection of performance indicators and quantification of performance objectives (Chen et al. 2005). Although China's current seismic design codes for hydraulic engineering (2015) partially adopt this concept, such as seismic design and verification, seismic safety assessment remains deterministic and lacks clear provisions, especially for earth-rock dams, particularly high-profile concrete faced rockfill dams. Therefore, it is necessary to conduct a seismic safety assessment of high-profile concrete faced rockfill dams from a performance probability perspective. In conclusion, the performance-based seismic safety assessment of high-profile concrete faced rockfill dams should primarily address the following issues: the true response behavior of structures under seismic actions should be reflected through effective seismic analysis models and methods; in practical applications, uncertainty factors should be thoroughly considered, and seismic response analysis should be conducted from a probabilistic standpoint; quantified performance objectives and rational performance indicators are prerequisites and foundations for seismic performance assessment. Consequently, the following section mainly provides a concise overview of the research trends in concrete faced rockfill dam studies based on these three key concerns of designers.
1.2.3 Performance-Based Seismic Design Framework
The performance-based seismic design framework for structural engineering can be succinctly summarized as follows: considering uncertainty factors under seismic actions, the structural design is tailored to meet various functional requirements, achieving an optimal balance between safety and economy. Furthermore, for complex engineering structures, the performance-based seismic safety assessment primarily encompasses three aspects: (1) analysis of various uncertain factors under seismic actions; (2) seismic response and probabilistic analysis; (3) seismic loss analysis. This process can be illustrated using Fig. 1.4 as a schematic (taking a high earth-rock dam as an example). Uncertainty factors encompass seismic motion and other load uncertainties, material parameter uncertainties, model uncertainties, and other uncertainties, etc. Seismic response and probabilistic analysis mainly involve conducting a series of response analyses for the structure under a range of seismic excitations, considering the aforementioned uncertainties, selecting appropriate performance indicators, and subsequently obtaining the probabilities of achieving different performance objectives. Seismic loss analysis refers to the calculation of various direct and indirect economic losses (including casualties) under different performance objective probabilities. However, the theory of performance-based seismic design is still in its early stages within the field of hydraulic engineering construction. Due to the significant complexity of dams, currently, no country in the world has utilized performance design theory for seismic design of dams. Therefore, it is necessary to conduct performance-based seismic safety assessments based on current conditions. Scholars in certain countries and regions have initiated relevant efforts or transitioned towards performance-based design (Chen 2010, 2005; Lin 2005, 2004; Zhang 2016).
A flowchart presents the steps involved in performance-based seismic safety assessment of high earth and rockfill dams. It starts with uncertainty factors, followed by nonlinear dynamic and seismic probability analysis, quantified performance objectives, and ends with seismic loss analysis. Includes factors such as ground motion, methods and models, dam deformation, slope stability, seepage body safety, losses, and optimal balance solution.
Fig. 1.4
Flow chart of performance-based seismic safety evaluation
A structural flowchart with 7 chapters focussing on aspects of seismic safety evaluation of high C F R Ds under random dynamic loads. It starts with traditional deterministic numerical analysis and then moves on to stochastic ground motion, earthquake ground motion-material parameter coupled randomness, and finally to engineering seismic codes.
Fig. 1.5
The research framework
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1.3 The Focus and Content of This Book
As mentioned earlier, the theory of performance-based seismic design has gradually been applied and developed in various engineering fields. However, for earth-rock dams, the current seismic safety assessment mainly relies on traditional deterministic analysis methods for simulation. Despite the initial forays into performance-based seismic safety assessment, especially concerning high concrete faced rockfill dams, research in this area remains relatively scarce. Current studies have also inadequately accounted for uncertainty factors under seismic conditions and have not conducted seismic safety analysis from a probabilistic perspective. Additionally, there is a lack of a systematic evaluation framework and system. Therefore, this section summarizes the existing research efforts, providing an overview of the main issues currently present. Addressing these issues, the main research content of this paper is introduced.
1.3.1 The Current Existing Problems
Based on three aspects of performance-based structural seismic safety assessment and considering the challenges posed by current disaster losses and impacts (Chen et al. 2010), this paper primarily addresses the uncertainties in seismic motion and material parameters under earthquake conditions, conducting seismic response and probabilistic analysis. The main issues are as follows:
(1)
Study on describing uncertainty of seismic motion and dam-building material parameters, as well as sample selection and generation. In seismic response analysis of high concrete faced rockfill dams, uncertainties exist in both seismic motion and dam-building materials. Currently, there is limited research that adequately considers the uncertainties in seismic motion and dam-building material parameters, especially the randomness of material parameters. Furthermore, the coupled stochastic effects of these two factors have not been effectively considered. Due to the high-dimensionality and diverse statistical distributions of stochastic parameters, commonly used methods for generating stochastic samples are not suitable for large and highly nonlinear high concrete faced rockfill dams. Therefore, it is necessary to comprehensively consider the influences of seismic motion randomness, dam-building material parameter uncertainty, and the coupled randomness of seismic motion and material parameters. This involves establishing a stochastic seismic motion model and a method for generating high-dimensional stochastic parameters. These steps are essential for conducting random dynamic and probabilistic analysis of high concrete faced rockfill dams.
(2)
Research on stochastic dynamic response and probabilistic analysis methods. Currently, there is limited research related to probabilistic analysis of earth-rock dams, especially concerning stochastic dynamic time history analysis. Traditional probabilistic analysis methods such as the first-order second-moment method, Monte Carlo method, response surface method, and their improved forms may struggle to acquire the stochastic dynamic information of structures. They might involve extensive computations, coupling with structural response analysis, continuous sample training, and iteration. These challenges make them less suitable for seismic stochastic dynamic response and probabilistic analysis of highly nonlinear, complex, and computationally extensive high concrete faced rockfill dams. As a result, it's essential to develop rational and efficient probabilistic analysis methods.
(3)
Research on refined stochastic dynamic time history analysis method based on elastic–plastic behavior and inconsistent seismic input. Currently, the stochastic dynamic and probabilistic analysis of earth-rock dams is generally based on equivalent linear and consistent seismic input, or quasi-static methods. However, under seismic actions, especially strong earthquakes, high concrete faced rockfill dams exhibit strong nonlinear characteristics, and research indicates that inconsistent seismic input significantly affects their dynamic response. Therefore, it's necessary to consider elastic–plastic behavior and inconsistent seismic input to conduct refined stochastic dynamic and probabilistic analysis of high concrete faced rockfill dams.
(4)
Selection of performance indicators and quantification of performance objectives, as well as research on performance-based seismic safety evaluation of high concrete faced rockfill dams. Currently, a consensus has been reached regarding the comprehensive evaluation of the seismic safety of high concrete faced rockfill dams from three aspects: dam deformation, dam slope stability, and seepage prevention. However, reasonable performance indicators and quantified performance objectives have not been systematically studied and discussed. Furthermore, based on these three aspects, there is limited research from the perspectives of stochastic dynamics and probability. Nevertheless, this is crucial for the performance-based seismic safety assessment of high concrete faced rockfill dams. Therefore, introducing the concept of performance-based seismic design, after thorough discussions on the selection of performance indicators and quantification of performance objectives, a framework for the performance-based seismic safety evaluation of high concrete faced rockfill dams is formulated.
1.3.2 Main Ideas and Tasks
In response to the aforementioned main issues, a performance-based seismic safety evaluation framework for high concrete faced rockfill dams is established, systematically considering the uncertainties under seismic actions. Addressing seismic motion randomness, dam-building material parameter uncertainty, and the coupled randomness of seismic motion and material parameters, a methodology is developed based on the hydraulic seismic design spectrum for generating stochastic seismic motions. High-dimensional stochastic parameter sample generation methods and seismic motion-material parameter coupled stochastic sample generation methods are established. Combining refined nonlinear finite element dynamic time history analysis methods, probability density evolution methods, and vulnerability analysis methods, the stochastic dynamic response characteristics of high concrete faced rockfill dams are studied from a probabilistic perspective.
Proposed seismic safety evaluation performance indicators for high concrete faced rockfill dams are suggested, along with corresponding performance levels that have probabilistic guarantees. Ultimately, a multi-seismic intensity-multi-performance objective-failure probability performance relationship is established. This forms a preliminary performance-based seismic safety evaluation framework that provides a scientific basis for the seismic design and performance control of high concrete faced rockfill dams. The main contents of this book encompass the following aspects:
This Chapter: This chapter provides a brief overview of the research background and significance of this paper. It introduces the content and development of performance-based structural seismic safety design and elaborates on the key issues in the seismic safety evaluation of high concrete faced rockfill dams based on performance criteria. It points out the main challenges existing in current research and introduces the research scope of this paper.
Chapter 2: This chapter briefly outlines the uncertain factors present in earth-rock dams under seismic actions and the main probabilistic analysis methods. It focuses on introducing the generalized probability density evolution method and its relevant application process. The process of generating stochastic seismic motion and high-dimensional stochastic samples is established. The effectiveness and reliability of the generalized probability density evolution method applied to large-scale geotechnical engineering are verified. This lays the theoretical foundation for subsequent analyses of stochastic seismic response and performance-based seismic safety evaluation of high concrete faced rockfill dams.
Chapter 3: This chapter comprehensively considers the randomness of seismic excitation, combining the generalized probability density evolution method with elastoplastic analysis. From the perspectives of stochastic dynamics and probability, it reveals the seismic response patterns of high concrete faced rockfill dams, forming the foundation for a performance-based seismic safety evaluation. The stochastic dynamic and probabilistic responses of several commonly used response variables in high concrete faced rockfill dams, including dam body acceleration, deformation, and panel stress, are examined. The numerical distribution ranges of these response indicators are studied from the viewpoints of stochastic dynamics and probability under various seismic intensities. Finally, based on performance indicators that combine dam top settlement deformation and the ratio of panel demand stress, along with cumulative over-stress duration, a preliminary performance-based seismic safety evaluation framework tailored to high concrete faced rockfill dams is established.
Chapter 4: This chapter combines the high-dimensional stochastic parameter sampling method based on the GF-deviation resampling technique with the generalized probability density evolution method. It uncovers the stochastic dynamic response and probabilistic characteristics of high concrete faced rockfill dams influenced by random factors in material parameters. Using the GF-deviation resampling technique for optimized point selection, elastoplastic stochastic parameter samples are generated. These samples are then combined with elastoplastic analysis for high concrete faced rockfill dams. The chapter delves into the stochastic dynamic response and probabilistic characteristics of high concrete faced rockfill dams under deterministic seismic actions, considering the impact of random factors in material parameters. The effects of different distribution types of stochastic parameters are also compared.
Chapter 5: This chapter systematically considers the coupled randomness of seismic motion and material parameters. It thoroughly investigates the impact of this coupling on the dynamic response and seismic safety of high concrete faced rockfill dams from the perspectives of stochastic dynamics and probability. This chapter further refines the performance-based seismic safety evaluation framework. By combining spectral representation-random function methods with random material parameter variables, both stochastic seismic motions and random material parameter samples are simultaneously generated. From the viewpoints of stochastic dynamics and probability, the chapter contrasts the effects of various stochastic factors, including seismic motion randomness, material parameter uncertainty, and the coupling of seismic motion and material parameters, on the seismic response of high concrete faced rockfill dams. The framework is extended to encompass a multi-seismic intensity-multi-performance objective-exceed probability performance relationship and fragility curves considering the coupled randomness of seismic motion and material parameters under different seismic intensity levels. This finalizes the refinement of the performance-based seismic safety evaluation framework.
Chapter 6: This chapter delves into the stochastic dynamic response patterns of three-dimensional high concrete faced rockfill dams. It primarily explores the selection of performance indicators and performance levels for panel safety assessment. It establishes a connection with the aforementioned performance safety evaluation framework and further enhances the performance-based seismic safety evaluation framework. This chapter serves as a scientific basis for the seismic design and performance control of high concrete faced rockfill dams.
Chapter 7: Departing from the perspective of current hydraulic seismic codes and engineering applications, this chapter systematically considers the randomness of seismic motion, material parameter uncertainty, and the coupling of seismic motion and material parameters. It explores a performance-based seismic safety evaluation framework for the slope stability of high concrete faced rockfill dams. Using the dynamic finite element time history method for slope stability analysis, coupled with soil softening strength change calculations, and incorporating the generalized probability density evolution method, the chapter evaluates the influence of rockfill material softening characteristics on the seismic safety stability of dam slopes from stochastic and probabilistic viewpoints. By considering safety factors, the cumulative time of safety factor exceeding limits, and cumulative slip displacement, the impact of material softening on dam slope seismic safety stability is assessed. Finally, a progressive development of probabilistic analysis methods for dam slope stability and a performance-based seismic safety evaluation framework for dam slope stability are established.
Chapter 8: Conclusion and Future Outlook. This chapter summarizes the research conducted in this paper, elucidates the main points of innovation, and outlines the primary directions and content for future research endeavors (Fig. 1.5).
The finite element static, dynamic, and stability calculations utilize the independently developed software tools, GEODYNA and FEMSTABLE 2.0, by the Institute of Engineering Seismic Research, School of Hydraulic Engineering, Dalian University of Technology. This software suite, supported by funding from more than 10 projects by the National Natural Science Foundation of China, incorporates numerous advantages and advanced constitutive relationships from various foreign geotechnical engineering analysis programs like FEMDAM, QUAD8, GEOSLOPE, and FLUSH. It encompasses over ten types of elements, including continuous block elements, interface elements, beam elements, column elements, mass elements, and boundary elements (viscous boundaries). This suite is developed using the Visual C++ platform, object-oriented design methods, and advanced technologies such as CPU + GPU parallel computing. Presently, this software suite has been applied in seismic calculations and analysis for dozens of major earth-rock dam projects, nuclear power plant projects, as well as significant water transportation projects such as ports, both domestically and internationally. It has gained extensive usage and accumulated rich engineering experience.
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