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PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON CIVIL AND STRUCTURAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping
A Limit Analysis Method for Nailed Earth Slopes
Department of Civil Engineering, Tamkang University, Taipei, Taiwan
Y.S. Hong, "A Limit Analysis Method for Nailed Earth Slopes", in B.H.V. Topping, (Editor), "Proceedings of the Eighth International Conference on Civil and Structural Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 107, 2001. doi:10.4203/ccp.73.107
Keywords: limit analysis, soil nailing, slip surface, earth slopes.
In this paper, a new stability analysis model based on the limit analysis concept for nailed earth slopes is presented. A plastic deformation mechanism that satisfies the boundary velocity conditions is assumed. By equating the external rate of work to the internal rate of dissipation in an assumed velocity field, a minimum safety factor and the corresponding critical slip surface can be obtained. The proposed model can be applied to vertical as well as non-vertical slopes using the method of slices. In order to promote calculating efficiency, the developed analysis model is implemented into a computer program called SASNS. Using this program to analyse a full-scale nailed wall built in France. The results are compared with the observation. The applicability of the proposed model has been proved in this paper.
In the literature, most design methods for nailed earth slopes are based on the limit equilibrium concept[1,2,3,4]. The major differences among these methods are the failure surfaces (i.e. bi-linear, parabolic, circular, log-spiral), the mechanism of soil and nail interaction, considering only axial force or both shear and axial forces in the nail. In addition, the definition of safety factor varies with the design approach. In recent years, nailed soil has been considered a composite material. The yield criteria for the materials and the corresponding interaction between them must be taken into consideration. Therefore, the required safety factor is different for various failure mechanisms. For example, the French method suggested a safety factor for soil strength and the nail pullout resistance equal to 1.5. But, the German method  assumed a safety factor for soil strength equal to 1.0 and for nail pullout resistance equal to 1.52.0. Additionally, Hong and Chen  showed the shearing resistance of soil mobilized almost fully for vertical nailed slopes through numerical simulation. Therefore, the safety factor for the soil is assumed to be 1.0 in this paper.
Although numerical methods can consider versatile constitutive relations of materials, they have difficulties in determining the input parameters as well as requiring extensive calculation time. Consequently, a simplified method adopting the concept of limit analysis from the plasticity theory is presented herein. Theoretically, the upper bound theorem requires satisfying the boundary velocity condition, as well as strain and velocity compatibility conditions. The internal dissipation of energy in the plastic flow associated with such a field can be computed from an idealized flow rule. In other words, the upper bound theorem considers only the kinematical mode and energy dissipation. The stress distribution need not be in equilibrium. On the contrary, the lower bound theorem considers only the equilibrium and stress boundary conditions. The exact solution will be between the two limits. If the assumed plastic deformation mechanism or the assumed stress field is close to the actual condition, the solution from the analysis will be close to the exact solution.
Since a nailed soil mass is a composite material, the stress distribution is very complex and difficult to determine. However, as stated above, the upper bound technique requires only considering a kinematical deformation field. Hence, this paper applies the upper bound theorem to present a limit analysis approach for analysing vertical and inclined nailed earth slopes. To verify the applicability of this model the predicted result will be compared with the observation of a full-scale nailed slope.
An efficient stability analysis approach for nailed earth slopes, capable of determining the minimum safety factor and the corresponding critical slip surface simultaneously, has been presented. The analytical model can consider the tensile resistance of the nail as well as its shear capacity. In addition to nail deformation at the limiting state, the effect of shearing dilation of soils is considered as well.
The result from analysing a test nailed wall using the proposed model shows good agreement in slip surfaces. However, as far as the safety factor is concerned, considering only tensile force in nails may obtain conservative solution.
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