#### Recommended Citation

Kim, D., and R. Salgado.*Limit States and Load and Resistance Design of Slopes and Retaining Structures*. Publication FHWA/IN/JTRP-2008/05. Joint Transportation Research Program, Indiana Department of Transportation and Purdue University, West Lafayette, Indiana, 2008. doi: 10.5703/1288284314326.

#### DOI

10.5703/1288284314326

#### Abstract

Load and Resistance Factor Design (LRFD) methods for slopes and MSE walls were developed based on probability theory. The complexity in developing LRFD for slopes and MSE walls results from the fact that (1) the representation of spatial variability of soil parameters of slopes using Gaussian random field is computationally demanding and (2) LRFD of MSE walls requires examination of multiple ultimate limit states for both external and internal stability checks.

For each design case, a rational framework is developed accounting for different levels of target probability of failure (or target reliability index) based on the importance of the structure. The conventional equations for loads and resistance in the current MSE wall design guides are modified so that the equations more closely reproduce the ultimate limit states (ULSs) in the field with as little uncertainty as possible. The uncertainties of the parameters, the transformation and the models related to each ULS equation are assessed using data from an extensive literature review.

The framework used to develop LRFD methods for slopes and MSE walls was found to be effective. For LRFD of slopes, several slopes were considered. Each was defined by the mean value of the strength parameters and unit weight of each soil layer and of the live load. (1) Gaussian random field theory was used to generate random realizations of the slope (each realization had values of strength and unit weight that differed from the mean by a random amount), (2) a slope stability analysis was performed for each slope to find the most critical slip surface and the corresponding driving and resisting moments, (3) the probability of failure was calculated by counting the number of slope realizations for which the factor of safety did not exceed 1 and dividing that number by the total number of realizations, (4) the mean and variance of the soil parameters was adjusted and this process repeated until the calculated probability of failure was equal to the target probability of failure, and (5) optimum load and resistance factors were obtained using the ultimate limit state values and nominal values of driving and resisting moments. For LRFD of MSE walls, (1) the First-Order Reliability Method was successfully implemented for both external and internal limit states and (2) a reasonable RF value for each limit state was calculated for different levels of target reliability index.

#### Report Number

FHWA/IN/JTRP-2008/05

#### Keywords

Load and Resistance Factor Design (LRFD), Slope, Mechanically Stabilized Earth (MSE) wall, Reliability analysis, Gaussian random field, Monte Carlo simulation, First-OrderReliability Method (FORM), SPR-2634

#### SPR Number

2634

#### Project Number

C-36-36MM

#### File Number

06-14-39

#### Performing Organization

Joint Transportation Research Program

#### Publisher Place

West Lafayette, Indiana

#### Date of this Version

4-2008