Three-Dimensional Hydromechanical Sectional Analysis of Cracked Nonprismatic Concrete Spillway Piers: Fid-Bau Portal

Three-Dimensional Hydromechanical Sectional Analysis of Cracked Nonprismatic Concrete Spillway Piers

Stefan, Lucian / Léger, Pierre

Abstract

Several concrete hydraulic structures, such as spillway piers, must be considered three-dimensional (3D) components subjected to 3D loads. A very convenient approach to perform stability analysis of concrete dams is the so-called gravity method, leading to the solution of a PMM problem (axial force $P$ and biaxial bending moments $M_{x}$ , $M_{y}$ ) assuming linear normal stress distribution. If cracking takes place, water penetrates into the cracks, inducing the development of full uplift pressures (UPs). Sliding safety factors (SSFs) are computed using shear force resultants $V_{x}$ , $V_{y}$ , and a Mohr-Coulomb failure criterion while ignoring torsion $T$ (VVT). This paper presents a 3D extension of the gravity method for cracked planar concrete sections of arbitrary geometry subjected to arbitrary loads (PMM-VVT). To compute the shear stress distribution, a VVT sectional analysis algorithm has been developed based on the theory of elasticity (TE), including Saint-Venant and warping torsional components combined with triangular 2D finite elements (FEs). Afterward, the SSF on the failure plane is computed from the integration of normal stresses on the remaining uncracked area where the Mohr-Coulomb criterion (considering the shear stresses from the VVT solution) has not been locally exceeded. Two validation examples and a case study of an actual pier are presented to illustrate the accuracy and efficiency of the proposed approach compared with full 3D FE analyses.