## 1 Introduction  
Concrete gravity dams are widely used due to their simple structure, safety, and reliability, strong adaptability to topographic and geological conditions. Numerous concrete gravity dams are in service in the world and are critical components of a nation's infrastructure. However, some of them are located in seismically active regions. Earthquakes may cause varying degrees of damage in concrete gravity dams. The presence of damage impairs the durability and operational performance of concrete gravity dams. Determinations of damage level are closely linked with the performance assessment of concrete dams. Traditional seismic damage classification methods are promoted based on the performance parameters of damage coefficient, energy dissipation, failure modes, and stress state, etc. These parameters are widely used in the field of damage of dams from earthquake waves, there are still some problems that need to be improved. For example, the stress state-based method tends to be localized, and it is difficult to reflect the global damage level; the determination of conversion coefficient between the local and global damage coefficients has a certain degree of subjectivity, and the calculation of intermediate variables is easily influenced by numerical simulation model and its parameters. It is well known that the displacement, as a daily monitoring physical quantity in dams, not only can reflect the behavior of dams directly but can be obtained conveniently and quickly. Therefore, establishing a classification method for evaluating the damage of dams based on the displacement is of great significance for the real-time assessment of dams after earthquakes.  
Fragility analysis is one of the key methods to evaluate the state of structures after the earthquake waves and has been widely concerned [1; 2; 3; 4; 5]. Performance parameter selection of damage degree and corresponding damage classification are the critical points when analyzing the seismic fragility analysis of concrete dams [6; 7]. Methods of failure modes-based [8], stress state on weak position-based [9], energy dissipation-based [10], performance-based [11] and the damage coefficient [12; 13] have been introduced and applied to study seismic fragility of concrete dams, respectively. Four (intact, slight, moderate, and severe) or five levels (slight, moderate, severe, destruction, and complete destruction) of seismic damage are used commonly in some standards [14; 15]. However, the determination of stress, energy dissipation, failure modes, and weight factors, and so on, may meet various challenges or not be readily available in time.  
Changes in stress, damage degree, and strength degradation can be directly reflected in the physical quantity of displacement. The objective of this paper is to study (1) the relationship between the residual displacement and the damage coefficient and (2) the residual displacement-based seismic damage classification method for gravity dams. The remainder of this paper is organized as follows. In Section 2, methods for expressing the relationship between the displacement and the damage are presented, and the fragility analysis method and process of dams are showed. In Section 3, first, a finite-element model of Guandi gravity dam is established, then the variation curves of displacements with the peak ground acceleration (PGA) are analyzed and the linear functional relationship between the displacement and the damage coefficient is proposed, finally, the residual displacement-based seismic damage classification method is proposed and the seismic fragility is analyzed and compared. In Section 4, some conclusions are presented.