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The actual dead load of an arch dam should be applied gradually through staged construction and sequenced grouting. However, the cantilever- and integral-type dead loads commonly used in the analysis of arch dams represent simplified versions of the actual loading. In this paper, these two types of dead loads, i.e. cantilever and integral types, are presented based on the Lagrange multiplier method considering the nonlinear behaviors of contraction joints. Based on the finite element method and an appropriate contact model together with artificial viscoelastic boundary conditions, a dynamic analysis model of a dam–foundation–reservoir system is established in consideration of the interactions between the arch dam and foundation, the opening and closing of contraction joints, and the radiation damping effect of the far-field boundary. Taking a 300 m high arch dam in the strong earthquake area of West China as an example, a fine mesh finite element model with a total of approximately 3.5 million degrees of freedom is established. The separate effects of the cantilever and integral dead loads on the static and dynamic responses of the dam are studied. The results demonstrate that the distribution and magnitude of the contraction joint opening width and maximum tensile stress are different under the two different dead load simplifications.

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Parameter uncertainty associated with concrete arch dams always arises from modeling assumptions and the lack of knowledge or information of the engineering geological situations, especially in the seismic stability analysis of arch dams. In this research, a high arch dam is selected as a case study for probabilistic analysis of the seismic stability performance. The arch dam abutment and the dam are coupled as a system. A comprehensive approach considering contraction joints, boundaries of the probable sliding rock mass and the dam-foundation interface is presented. The contact nonlinearity is solved by using the dynamic contact model with Lagrange multiplier method. The main parameters of the probable sliding block are considered as random variables containing the friction coefficients and cohesions. Both the slippage and sliding area ratio are chosen as the engineering demand parameters (EDP). The sensitivity analysis is performed to reveal the relative influence of each parameter separately by the approximate incremental dynamic analysis (IDA) method. The friction coefficients are shown to be more crucial than the cohesions on the dam’s resistance to seismic instability. The sliding area ratio can be better used for unveiling the sliding process of the arch dam of concern, while the slippage is useful for one to judging the stability of the arch dam under seismic hazards. The Latin hypercube sampling (LHS) with approximate moment estimation is used to investigate the parameter uncertainty to the seismic stability performance of the high arch dam. The results provide a useful reference for using the median/mean-parameter model to accurately estimate the median/mean response of the dam.