Simplified Model for the Hybrid Method to Design Stabilising Piles Placed at the Toe of Slopes

Stabilizing precarious slopes by installing piles has become a widespread technique for landslides prevention. The design of slope-stabilizing piles by the finite element method is more accurate comparing to the conventional methods. This accuracy is because of the ability of this method to simulate complex configurations, and to analyze the soil-pile interaction effect. However, engineers prefer to use the simplified analytical techniques to design slope stabilizing piles, this is due to the high computational resources required by the finite element method. Aiming to combine the accuracy of the finite element method with simplicity of the analytical approaches, a hybrid methodology to design slope stabilizing piles was proposed in 2012. It consists of two steps; (1): an analytical estimation of the resisting force needed to stabilize the precarious slope, and (2): a numerical analysis to define the adequate pile configuration that offers the required resisting force. The hybrid method is applicable only for the analysis and the design of stabilizing piles placed in the middle of the slope, however, in certain cases like road constructions, piles are needed to be placed at the toe of the slope. Therefore, in this paper a simplified model for the hybrid method is dimensioned to analyze and design stabilizing piles placed at the toe of a precarious slope. The validation of the simplified model is presented by a comparative analysis with the full coupled finite element model.

In general, the Design methods for slope stabilizing piles are: pressure or displacement-based method, and numerical methods. In 2012, Kourkoulis et al. proposed a hybrid method for the design of slope-stabilizing piles. This method merges the accuracy of the finite element method with simplicity of the analytical approaches. However, the hybrid method was only developed to analyze piles placed in the middle of unstable slopes.

The hybrid method for analysis and design of slope stabilizing piles
The hybrid method for the design of slope-stabilizing piles was proposed by Kourkoulis et al. in 2012. It consists of two steps; (1): an analytical estimation of the resisting force needed to stabilize the precarious slope, and (2): a numerical analysis to define the adequate pile configuration that offers the required resisting force for a desired pile head displacement.
In the analytical part, the estimations of the needed resisting force to stabilize the precarious slope is done by the conventional slope stability techniques. However, in the numerical part, Kourkoulis et al. proposed a new approach. This approach aims to reduce the numerical cost by reducing the size of the model; so instead of modeling the entire slope-piles system, only two piles and the surrounded soil are modeled as presented in figure 1.  [12].
The length of the simplified model is 10D, and its width is 2S (two times the spacing between piles). In full scale, it is assumed that the slope is reinforced by a row of piles with spacing S repeated indefinitely. Hs is the sliding depth, and Le represents the pile length.
For piles placed in the middle of precarious slopes, it was found that beyond a distance of 5D up-slope of the piles row, the soil displacement profile becomes almost uniform [12]. Therefore, 10D (2 times 5D) was chosen to be the length of the simplified model.
The Hybrid method was developed to design piles placed in the middle of the slope, but in certain cases like road constructions, piles are needed to be placed at the toe of the slope. Therefore, in this paper a simplified model for the hybrid method is dimensioned to analyse and design stabilizing piles placed at the toe of a precarious slope.
3 Investigation of the uniformity of soil displacement profile for piles placed at the toe of the slope

Properties of slopes and piles
In order to investigate the uniformity of soil displacement profile for piles placed at the toe of the slope, different slope geometries with pre-existing potential sliding interface (PEPSI) were tested, with inclination angle ranging from 21° to 26° and pile spacing of 3D and 4D.
For the unstable and the stable parts of the slopes, soil properties are resumed in table 1. Soil is simulated with an elastoplastic model (Mohr-Coulomb failure criterion).

The numerical analysis
Fully coupled slopes with pre-existing potential sliding interface (PEPSI) were analyzed using finite element code Abaqus, an example is presented in figure 2.

Fig. 2.
Finite element mesh of the fully coupled slope reinforced by two piles with preexisting potential sliding interface (PEPSI).

Results and discussions
By analysing the displacement profiles, the following results were obtained: Figure 3 represents the displacement profiles at a distance of 5D up-slope of the piles.

Fig.3.
Soil displacement profiles at a distance of 5D up-slope of the piles row for different slopes inclinations, and pile spacings of 3D and 4D.
One can notice that either for pile spacing of 3D or 4D, the soil displacement profile at a distance of 5D upslope of the piles is almost uniform. Figure 4 represents a cut at a distance of 5D upslope of piles with soil displacement contours.

The simplified model for the hybrid method to design stabilizing piles placed at the toe of slopes
As found above, the soil displacement profile at a distance of 5D up-slope the row of piles is almost uniform. Therefore, the simplified model for the hybrid method to design stabilizing piles placed at the toe of slopes is identical to that developed by Kourkoulis et al. in 2012, The length of simplified model is 10D, and its width is 2S, as shown in figure 1.

Validation of the simplified model against fully coupled reinforced slope analysis
In order to validate the simplified model, a fully coupled analysis was conducted first, it consists of a slope with 24° inclination reinforced by a row of concrete piles of 1.2 m diameter, and spacing S=3D. Then a simplified model was analysed as presented in figure 5.

Results and discussions
For the fully coupled model, the pile head deflection necessary to stabilize the slope by coupled methodology was found to be 6.3 mm.
Using the method of slices, it was found that the required resisting force (RF) needed to stabilize the slope is 341 KN/m. After the analysis of the simplified model, the needed RF (341 KN/m) was given by the piles at a pile head deflection of 7.4 mm, with an error of 17%.

Conclusions
In this research about the simplified model for the hybrid method to design stabilizing piles placed at the toe of slopes, the following conclusions were reached: The displacement profile at a distance of 5D up-slope the pile location may be considered as uniform.
The simplified model for the analysis and the design of slope stabilizing piles placed at the toe of the slope is identical to that of piles located in the middle of the slope.