Finite Element Modeling of Reinforced Concrete Structural Walls for Performance-Based Seismic Design

Abstract

A novel finite element modeling approach for nonlinear analysis of reinforced concrete (RC) structural walls is developed and implemented in OpenSees, which is an open-source computational platform widely used in earthquake engineering. The proposed analytical model incorporates a twodimensional RC constitutive panel behavior described with the fixed-strut angle model into a fournode isoparametric quadrilateral finite element model formulation. The modeling approach is used to simulate the responses of two medium-rise RC wall specimens (aspect ratios of 1.5 and 2.0) with predominant shear-flexure interaction responses. Based on detailed comparison of experimental and analytical wall responses, the model is found to be capable of predicting accurately the experimentally-measured response attributes of the cyclic nonlinear wall behavior including lateral strength, stiffness, stiffness degradation, as well as their hysteretic response characteristics. The model also captures interaction between flexural and shear behavior, and provides accurate estimates of the relative contribution of nonlinear flexural and shear deformations to wall lateral displacements and their distributions over the wall height. Finally, the proposed modeling approach describes reasonably well local response characteristics including magnitudes and distributions of strain and stress fields, as well as cracking patterns. Based on the response comparisons presented, model capabilities are assessed and possible model improvements are identified.

Numerical model of time-dependent diffusion of chlorides in the concrete based on 2D four-node isoparametric element

“…Jacobian J has the form of matrix two by two and its individual members can be expressed by equations: (9) For calculation the original matrix form of Jacobian J is needed: (10) and also, the inverted matrix: (11) where the Jacobian determinant is calculated using Sarrus rule [29]: (12) The original shape functions (1) have been derived by formulas and the matrix of shape functions has been obtained: (13) Equation 8can be written in a simplified matrix as follows: (14) The last step of finite element analysis is the derivation of the conductivity matrix, which is analogous to the stiffness matrix in classical problems of elasticity theory, and therefore is denoted by K. For nonlinear diffusion problem is needed to derive also the matrix of capacity C. In publication [23], both matrices were derived for a triangular element and had the following form:…”

“…It should be noted that the newly developed algorithm contains all important formulas and expressions. The formulas related to the calculations of Jacobian J (9), (10), (11), (12), the matrix of the shape functions N (13) and the gradients of these functions B (14) have been applicated. Finally, the equations for conductivity matrix K (17) and capacity C (18) enter the calculation.…”

“…The finite element model (FEM) is based on the newly derived four-node isoparametric diffusion element that has not been published yet in this form, up to author knowledge. Similar elements are used for solving problems of statics and dynamics, or heat [10,11], but so far they have not been introduced for the process of diffusion of chloride ions in concrete. The following text is a brief overview of the methodology, derivation of the finite element, and an example with comparison of results to analytical solution of the 2D diffusion.…”