Analysis of resistance factors for LFRD of soil nail walls against external stability failures

Abstract

This paper presents reliability analyses of soil nail walls against two external ultimate limit states, global and sliding stabilities, which are related to the external stability failures of soil nail walls. Reliability analyses are conducted using Monte Carlo simulation technique. Soil nailing is a popular retaining system in highway construction and slope stabilization, and its current design practice is still based on the working stress design. There remains a need to establish a more rational design framework—load and resistance factor design—based on the concept of limit state design and reliability analysis for soil nail walls. The development of load and resistance factor design approach must consider multiple ultimate limit states, associated with external, internal, and facing failures. The analyses of resistance factors against two external failures are conducted in this study considering various influencing factors, including statistical parameters of soil friction angle, ultimate bond strength between soil and nails, soil type, wall geometry (wall height, back slope angle, and face batter angle), and nail configurations (nail inclination angle, drillhole diameter, and nail spacing). In the end, a series of resistance factors are proposed for potential application of load and resistance factor design approach against external failures for soil nail walls according to different design codes.

Appendix

$\begin{aligned} B_{L} &= \frac{\cos (\alpha - i)L}{\cos \alpha }; \\ H_{eff} &=\, H + \left( {B_{L} - H { \tan }\alpha } \right) { \tan } \theta ; \\ K_{a}& =\, \frac{{\sin^{2} (\omega + \phi^{{\prime }} )}}{{\sin^{2} \omega \sin (\omega - \delta^{{\prime }} )\left[ {1 + \sqrt {\frac{{\sin (\phi^{{\prime }} + \delta^{{\prime }} )\sin (\phi^{{\prime }} - \theta )}}{{\sin (\omega - \delta^{{\prime }} )\sin (\omega + \theta )}}} } \right]^{2} }} \\ \end{aligned}$ where $\omega = 90^{\text{o}} + \alpha$, δ’ is the angle of friction between the soil and the wall, in this paper, it is conservatively assumed as zero; $L_{e} = L - \frac{\cos (\alpha + \psi )}{\sin (\psi + i)\cos \alpha }h_{j} ,$ where h _j is the vertical distance from the j-th nail head to the base of the wall; $L_{f} = \frac{\cos (\alpha + \theta )}{\sin (\psi - \theta )\cos \alpha }H;$

$$Q_{s} = \frac{\cos (\alpha + \psi )\cos \theta }{\cos (\alpha + \theta )}L_{f} q_{s} ;$$

$$T_{nail} = \sum\limits_{j = 1}^{n} {L_{e} } \frac{{\pi D_{DH} q_{u} }}{{S_{h} }};$$

$$W_{GL} = \frac{\cos (\alpha + \psi )}{2\cos \alpha }HL_{f} \gamma ;\;{\text{and}}\;W_{SL} = \frac{\gamma }{2}\left[ {H_{eff}^{2} \cot \theta + H^{2} (\tan \alpha - \cot \theta )} \right].$$