Construction of tunnels and small- to medium-span bridges is a $12 billion per year industry in the United States, with a significant portion going into buried arch structures. Notwithstanding such expenditure, modern arch design and construction, in many cases, is highly conservative. This is because the closed-form solutions used by most designers today do not correctly account for soil-structure interaction. In fact, soil-structure interaction makes a closed form solution impossible. With the advent of high power computers in recent years, some designers have turned to finite element (FE)modeling as the main vehicle of analysis. Such numerical procedures provide an accurate approximation of physical behavior. Practices using FE analysis for buried arch design almost exclusively use two-dimensional models because they are faster to set up and analyze than three-dimensional models and cost substantially less. However, 2-D models fail to account for the stiffness of the structure and spread of discrete loads in the third-dimension. Both the 1996 and 1998 AASHTO-LRFD Bridge Design Specifications address this problem, providing methods of load reduction. Much of the current reduction, however, is based on research done on concrete bridge decks, and does not account for continuous elastic support or the geometry of the structure. This results in a conservative analysis at low fill covers (<10') and/or increasing spans (>20’). This research provides a method to rectify the discrepancy that arises in discrete loading of 2-D FE models of semi-flexible buried concrete arch bridge, culvert, and tunnel systems due to the plane-strain assumption. Rectification is accomplished by providing a correlation between the deflection of a beam-on-elastic-foundation analysis and a distribution length by which the load in 2-D analysis is reduced. Distribution lengths are derived using bending energy ratios. The correlation considers structural geometry, overburden height, and base soil stiffness. Reduction of the 2-D design load by the proposed distribution length results in shear forces and bending moments nearly equivalent to those obtained from 3-D analysis in the plane of discrete load application transverse to the structure. Less conservative results are also obtained for axial forces. These results are intended for use on structures that are four times the span in length, or longer.



College and Department

Ira A. Fulton College of Engineering and Technology; Civil and Environmental Engineering



Date Submitted


Document Type





soil-structure interaction, load spread, live load reduction, buried, concrete, arch, culvert, finite element analysis, distribution width, distribution length