Boundary setting method for the seismic dynamic response analysis of engineering rock mass structures using the discontinuous deformation analysis method

Abstract

SUMMARYLarge deformations and discontinuous problems can be calculated using the discontinuous deformation analysis (DDA) method by solving time steps, and this method is suitable for simulating the seismic dynamic response of engineering rock mass structures. However, the boundary setting must be carefully analyzed. In this paper, four boundary settings for the DDA method are investigated. First, the contributions to the DDA equations for nonreflecting boundaries (including the viscous boundary and the viscoelastic boundary) are deduced based on the Newmark method. Second, a free-field boundary is introduced in the DDA method with boundary grid generation and coupling calculation algorithms to accurately simulate external source wave motion, such as earthquakes. Third, seismic input boundary treatments are intensively examined, and the force input method is introduced based on nonreflecting boundaries. Finally, the staticdynamic unified boundary is implemented to ensure consistent boundary transformation. The boundary setting method in the DDA method is discussed, and the suggested treatments are used to analyze the seismic dynamic response of underground caverns.

Boundary settings for the seismic dynamic response analysis of rock masses using the numerical manifold method

“…Assume a pair of dashpots is applied at point ( x , y ), the viscous normal traction σ n and shear traction τ s can be expressed as where a and b are absorption coefficients of the viscous boundary (in a standard viscous boundary, values of a and b are all set as 1); ρ is the density of the medium; v n and v s are the normal and shear velocities at ( x , y ).…”

“…Based on Equations and , viscous forces can be expressed as where l is the length of the viscous boundary.…”

“…There are 2 algorithms to obtain the seismic dynamic response of a free field. The first algorithm is based on the theoretical solution.…”

Application of the discontinuous deformation analysis method to stress wave propagation through a one-dimensional rock mass

“…Relative to previous studies, 31 the viscous boundary implemented by this paper is more efficient and has a high absorption precision. 25 Based on the viscous boundary, a force input method is used for inputting the incident wave. 23 The normal and tangential components of the velocity time history of the incident wave are transformed to the corresponding stress components:…”

“…[17][18][19] Additionally, to meet the demands of specific engineering problems, researchers can expediently modify the original DDA program with an open source code. [20][21][22] The authors [23][24][25] have developed the DDA method by modifying the boundary setting and stress wave inputting. These modifications enable DDA study the stress wave propagation across the rock mass.…”