Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 721602, 12 pages

http://dx.doi.org/10.1155/2015/721602

## Mechanism Research of Arch Dam Abutment Forces during Overload

^{1}College of Civil and Architecture Engineering, Guangxi University of Science and Technology, Liuzhou 545006, China^{2}College of Materials Science and Engineering, Guangxi University, Nanning 530004, China^{3}College of Civil and Architecture Engineering, Guangxi University, Nanning 530004, China

Received 5 September 2014; Revised 8 February 2015; Accepted 18 February 2015

Academic Editor: Paolo Lonetti

Copyright © 2015 Yu Xia et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper presents research on the abutment forces of a double-curvature arch dam during overload based on numerical calculation results obtained through finite element method by Ansys. Results show that, with an increase in elevation, the abutment forces and bending moment of the arch dam increase first and then decrease from the bottom to the top of the dam. Abutment forces and bending moment reach their maximum at the middle or middle-down portion of the dam. The distributions of abutment forces and moment do not change during overload. The magnitude of each arch layer’s forces and moment increases linearly during overload. This result indicates that each arch layer transmits bearing loads to the rocks of the left and right banks steadily. This research explains the operating mechanism of an arch dam under normal and overload conditions. It provides a simple method to calculate the distribution of forces and and a new method to calculate the overload factor of an arch dam through the estimation of arch layers based on the redistribution characteristic of arch abutment forces.

#### 1. Introduction

The development of arch dams has a long history that dates back to 1st century BC [1]. Relative uniformity was achieved in the 20th century after several designs and techniques were developed. The first known arch dam, Glanum Dam, was built by the Romans in France [2]. Arch dam is a type of dam curved in the shape of an arch, with the top of the arch pointing back into the reservoir. Thus, the force of the water against it, known as hydrostatic pressure, presses against the arch. An arch dam is most suitable for narrow gorges with stable rocks. Considering that arch dams are thinner than any other dam type, they require much less construction materials, which make them economical and practical in remote areas. Arch dams are built all over the world because they are safe and involve minimal cost [3]. China has the most number of arch dams [4]. Many numerical methods are currently applied to the analysis of the structure of arch dams. Some examples of these methods are finite element method [5–7], discrete element method [8, 9], block element method [10, 11], discontinuous deformation analysis [12], fast Lagrange analysis of continua [13], and interface element method [14]. Self-adapt element [15–17], meshless [18], and extended finite element methods [19–21] are utilized to simulate the development of cracks in the structure analysis of arch dams. The arch dam is a highly statically indeterminate structure. Through an arching action, arch layers transmit upstream water pressure to bank rocks on two sides. Arch layers play an important role in the safe operation of such dams, which transfers the loads to two banks. It makes large areas of arch dam body under compression through arch layer. This type of structure can make full use of compression strength of concrete. Limit equilibrium method is usually employed in the safety evaluation of arch dams [22, 23]. Little attention is paid to abutment forces in arch dam safety analysis. The mechanical characteristics of a structure can be determined through research on arch abutment forces during overload. It shows that thrust angles at different elevations increase during overload through abutments force analysis [24, 25]. Studying abutment force would thus provide a comprehensive understanding of the overload mechanism of arch dams.

#### 2. Concrete Cracking Simulation of Arch Dam during Overload [26]

##### 2.1. Concrete Cracking Mode

Before the failure of concrete under tensile condition, a linear relationship exists between stress and strain. The stiffness matrix iswhere is Young’s modulus for concrete and is Poisson’s ratio for concrete.

The following conditions apply to cracks in one direction only.

If principal stress in one direction is greater than the failure tensile stress, tensile failure occurs. After developing cracks, the concrete becomes an orthotropic material. Given that the stiffness and shear stiffness reduce the normal plane, the stress-strain matrix will change. After the destruction of the concrete, the presence of a crack at an integration point is represented through modification of the stress-strain relations by introducing a plane of weakness in a direction normal to the crack face. A shear transfer coefficient is introduced to represent a shear strength reduction factor for subsequent loads that induce sliding (shear) across the crack face. The stress-strain relationship is built in the direction of the failure surface and the direction perpendicular to it. When principal stress is greater than the tensile breaking stress in only one direction, the stress and strain of the new matrix arewhere the superscript signifies that the stress-strain relations refer to a coordinate system parallel to principal stress directions with the axis perpendicular to the crack face. works with adaptive descent and diminishes to 0.0 as the solution converges.

In Figure 1, is uniaxial tensile cracking stress and is the multiplier for the amount of tensile stress relaxation.