Abstract
This chapter deals with the application of experimental design in slope stability analysis. In particular, focus of the present chapter is on the application of Box-Behnken statistical design for assessment of stability of slopes in homogeneous soil (general case), for estimation of slope stability in clay-marl deposits at the edge of Neogene basins (case study) and for the extension of grid search method for locating the critical rupture surface. Extensive statistical analysis, internal and external validation imply high estimation accuracy and reliability of developed mathematical expressions for slope safety factor and for parameters of location of critical rupture surface. Main advantages and limitations of the proposed approach are thoroughly discussed with suggestions for main directions of further research.
TopIntroduction
In present chapter, potential application of a statistical design in stability analyzes of soil slopes is examined through three stages:
In the first stage, analytical model for prediction of slope safety factor is proposed as a function of slope geometry (slope height H and slope inclination β), soil properties (unit mass γ, soil cohesion c and angle of internal friction φ) and water conditions (pore water pressure coefficient ru). As a reader will see, developed model represents a simple mathematical expression of higher prediction accuracy when compared to the existing models. Results obtained imply a positive effect of shear strength parameters and negative effect of slope geometry, unit mass and water conditions on slope stability. Thereby, positive effect of a single parameter on slope stability actually implies that slope stability increases with the increase of the chosen parameter value. On the other hand, negative impact of a certain parameter indicates a decrease of slope stability with the increase of a parameter value. Results of the performed analysis also indicate that the impact of soil cohesion depends on the slope geometry, unit mass and angle of internal friction. Also, the influence of angle of internal friction is conditioned by the slope inclination and water conditions.
In the second stage, derived model describes the impact of main properties of clay-marl deposits on slope stability at the edge of Neogene basin in Belgrade (Serbia). Derived model is defined as a nonlinear function of the same slope and soil parameters as in the first stage, including the effect of bedrock depth d by introducing the dimensionless parameter d/H. Results obtained indicate that all examined properties of clay-marl deposits have a statistically significant impact on slope stability. Thereby, linear effect of influential parameters is predominant, while slope geometry and soil cohesion also show significant quadratic influence. Results of the performed research further indicate that the effect of slope height on its stability strongly depends on slope inclination, soil cohesion and bedrock depth. On the other hand, impact of slope inclination on its stability is influenced by soil cohesion and bedrock depth.
In the third stage, statistical design is used for extension of grid search method for locating the rupture surface. This is done by deriving separate analytical expressions for slip center grid (xmin, ymin; xmax, ymax), where one could expect to find a global minimum of slope safety factor. For the determined slip center grid, separate prediction models are derived for the corresponding ranges of slope safety factor and slip circle (rupture surface) radius. Developed mathematical expressions describe the dependence of slope safety factor on the same parameters of slope geometry, soil properties, water conditions and soil geneity as in the second stage. Obtained results indicate strong linear and quadratic effect of slope inclination on the location of slip center grid and corresponding safety factor. Moreover, location of slip center grid is strongly dependent on the slope height and angle of internal friction, latter of which also affect the value of slope safety factor in co-action with soil cohesion. Results of the analysis also imply that the effect of slope inclination is strongly affected by slope height, bedrock depth, water conditions and angle of internal friction. Impact of cohesion is conditioned by the influence of unit mass and slope height.
The main goal of this chapter is to provide a basic insight into the essence of the statistical design and its potential use in geotechnical practice. In particular, results obtained indicate that application of statistical design in slope stability analysis results in development of convenient prediction models for slope safety factor and for the location of critical slip surface, enabling in the same time the estimation of the effect of geometrical properties (slope height and inclination), soil properties (unit mass, soil cohesion and angle of internal friction), water conditions (pore water pressure coefficient) and soil geneity (homogeneous soil and the impact of bedrock depth) on the slope stability.
Key Terms in this Chapter
Rupture Surface: Surface of contact between the displaced material (landslide) and the intact soil.
Slope Safety Factor: A ratio of sums of stabilizing and destabilizing forces acting on a slope.
External Validation: Verification of the derived mathematical expression for the values of input factors which were not used for model development.
Internal Validation: Verification of the derived mathematical expression for the values of input factors used for model development.
Box-Behnken Design: A method for designing optimal experimental setup which examines each influential factor on three levels.
Grid Search Method: A method for locating the critical rupture surface, based on a construction of rectangular area, with a predefined grid. For each grid node, and for a predefined radius range, a minimum slope safety factor is determined, and ascribed to a node. After this process is finished for all the nodes in the grid, one is able to construct isolines-contours joining the nodes with the same value of safety factor.
Slope Stability Analysis: Analysis of the forces and moments acting on a slope, with the final results in a form of safety factor against the sliding and the location of the potential rupture surface.
Pore Water Pressure Coefficient: Dimensionless coefficient defined as a ratio of the pore pressure and normal stress at a certain point within a slope. When slope is dry, r u =0; when the groundwater is at the surface of the slope - r u =0.5.
Soil Geneity: A property of the soil regarding the difference of characteristics at each point within a soil. If the soil characteristics are the same for each point, then it could be treated as homogeneous. On the other hand, if soil characteristics are different at each point, then it is treated as heterogeneous.