An Extension of Marston’s Solution for the Stresses in Backfilled Trenches with Inclined Walls

Infrastructure rehabilitation and development are very active fields around the world. Many of these activities involve the installation of conduits buried in trenches. The analysis and design of such conduits often rely on a solution developed by Marston and his coworkers who used the basic arching theory proposed by Janssen. This solution is theoretically only valid for vertical trenches, but it has been used for trenches with different wall inclinations, which sometimes leads to non-conservative stresses. In this paper, a more general solution for the stress state in backfilled trenches is developed based on the approach adopted by Marston and his coworkers. The effects of wall inclination and of a surcharge on top of the backfill are introduced in the analytical solution. Numerical modeling is performed and the results are used to adjust some components of the equations, leading to a more general solution. The good correlation between the vertical stress distributions given by the proposed solution and additional numerical simulations indicates that this new solution is representative of the stress state in backfilled trenches, and can thus be used for the design of infrastructure rehabilitation and development.

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