Soil Dynamics and Earthquake Engineering 140 (2021) 106477 Available online 28 October 2020 0267-7261/© 2020 Elsevier Ltd. All rights reserved. Modifcation of direct-FE method for nonlinear seismic analysis of arch dam-reservoir-foundation system considering spatially varying ground motion Mehdi Varmazyari * , Saeed-Reza Sabbagh-Yazdi Structural Engineering Department, Faculty of Civil Engineering, K. N. Toosi University of Technology, Tehran, Iran A R T I C L E INFO Keywords: Nonlinear seismic analysis Concrete arch dam Spatially varying ground motion Non-stationary frequency content Absorbing boundaries Effective earthquake forces ABSTRACT The present paper aims to modify an existing direct fnite element method for nonlinear seismic analysis of high arch dam-reservoir-massed foundation systems to consider the effects of spatially varying ground motion at the bottom of the foundation rock with the non-stationary frequency characteristics. Viscous-damper boundaries are used to model the semi-unbounded foundation rock and the reservoir domains. In the existing direct fnite element method, it is assumed that incident waves propagate vertically upwards from beneath the foundation rock towards the ground surface, and the effective seismic forces starting from the control motion on the foundation surface are applied to the bottom and the side vertical boundaries of the foundation rock. Three components of the motion recorded at Parkfeld fault zone 16 during the 1983 Coalinga earthquake are selected as the free-feld control motion at the surface of the foundation rock. On the other hand, in the modifed direct FE method, fully non-stationary spectrum-compatible ground motion time histories, including both wave passage and incoherency effects, are simulated at a number of locations at the foundation bottom. Then the generated ground motions are used as multiple input incident motions to compute effective seismic forces applied to the bottom and the side boundaries of the foundation rock in the dam-reservoir-massed foundation system. Step-by- step procedures for computing the effective earthquake forces in the existing and the modifed direct FE methods are presented. The nonlinearity originates from opening/sliding of the vertical contraction joints within the dam body. The reservoir–structure interaction is accounted for via the fnite element method assuming compressible reservoir. The Karoun-I, a double curvature high arch dam, is selected as a case study. Several numerical vali- dation models are conducted and compared with the benchmark solutions to indicate the accuracy of the existing direct FE method. It was seen that applying effective earthquake forces determined from the modifed direct fnite element method increases the nonlinear seismic response of the dam-reservoir-massed foundation system in terms of the crest displacements and stress levels. 1. Introduction Generally, in seismic analysis of arch dams, it is assumed that the excitations along the base are identical, but earthquake ground motions due to long interface with the ground, vary with time and in space. To represent more reliable seismic response of concrete arch dams, some signifcant factors should be considered including: dam-foundation interaction; nonlinearities originated from opening/slippage of vertical contraction joints; a proper earthquake input mechanism; and spatial variation in the ground motion and its non-stationary feature effects. In the case of simulating spatially varying ground motions, some researchers proposed different stochastic models, however, they have shortcomings due to their restriction to linear structures [1,2]. Among these models, the spectral representation is the most used approach [3, 4]. Gao et al. [5] simulated ground motions with decomposition of lagged coherency matrix making higher accuracy than cross spectral density matrix. In addition, in the model introduced by Deodatis [6], the power spectral density (PSD) of the vector process is updated in an iterative scheme. This approach was extended so that the initial PSD could be estimated with fewer iterations [7,8]. Some methods have been presented with the aim to generate spatial variation in the ground mo- tions compatible with the predefned accelerations and coherency model * Corresponding author. E-mail address: me.varmazyar@gmail.com (M. Varmazyari). Contents lists available at ScienceDirect Soil Dynamics and Earthquake Engineering journal homepage: http://www.elsevier.com/locate/soildyn https://doi.org/10.1016/j.soildyn.2020.106477 Received 18 December 2019; Received in revised form 12 October 2020; Accepted 21 October 2020