Extension of the Gravity Method for 3D Cracking Analysis of Spillway Piers Including Uplift Pressures

The classical structural stability evaluation of concrete hydraulic structures, such as spillways, is based on the application of rigid body equilibrium to compute force and moment resultants, and in most instances beam theory assuming linear stress distribution. The computations are done supposing a symmetric structure subjected to load acting in the upstream/downstream direction leading to a unidimensional axial force $\left(P\right)$ -bending moment $\left(M\right)$ interaction problem. However, several load conditions (ice floes, earthquakes) could apply transverse force components leading to a nonlinear biaxial flexural problem $\left(P\text{-}{M}_x\text{-}{M}_y\right)$ taking into account the potential cracking of the sections, as well as pressurized water penetration in cracks. A three-dimensional extension of the gravity method is presented herein for arbitrary sections such as those of spillway piers. Robust algorithms based on the strength of materials have been developed to compute the kernel of arbitrary sections, locate the neutral axis (NA), and determine the normal stress distribution all of this considering a coupled biaxial hydromechanical interaction problem. Five validation examples will be presented as well as a case study on an actual spillway to illustrate the convergence of the proposed algorithms. It is possible to obtain, in certain instances, a nonconverging oscillatory response for the location of the NA. In this case, a heuristic approach is proposed to obtain a conservative equilibrium solution.