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Piles are extensively used as a means of slope stabilization. A novel engineering technique of truncated piles that are unlike traditional piles is introduced in this paper. A simplified numerical method is proposed to analyze the stability of slopes stabilized with truncated piles based on the shear strength reduction method. The influential factors, which include pile diameter, pile spacing, depth of truncation, and existence of a weak layer, are systematically investigated from a practical point of view. The results show that an optimum ratio exists between the depth of truncation and the pile length above a slip surface, below which truncating behavior has no influence on the piled slope stability. This optimum ratio is bigger for slopes stabilized with more flexible piles and piles with larger spacing. Besides, truncated piles are more suitable for slopes with a thin weak layer than homogenous slopes. In practical engineering, the piles could be truncated reasonably while ensuring the reinforcement effect. The truncated part of piles can be filled with the surrounding soil and compacted to reduce costs by using fewer materials.

The use of piles for stabilizing active landslides and as a preventive measure in the stable slopes has been considered a reliable and effective technique and has been implemented successfully in a number of applications over the last few decades, for example, [

The stabilization of unstable slopes with piles is complicated by factors affecting pile performance under the loading conditions of slope reinforcement and factors controlling the effect of piles on global slope stability. The current design practices for pile-reinforced slopes often use the limit equilibrium methods, where the soil-pile interaction is not considered, and the piles are assumed to only supply an additional sliding resistance. Ito and Matsui [

To better simulate the actual mechanism of failure, numerical methods including the finite element method and the finite difference method have been developed quickly and are becoming increasingly popular for piled slope analysis based on the shear strength reduction method. Chow [

Complicating the issues of pile-stabilized slopes including prediction of load distribution along piles were effects of soil type, pile size and spacing, pile orientation, truncating of piles, and so on [

The problem definition is given in Figure

Comparison of conventional stabilizing piles and truncated piles.

Conventional stabilizing piles (full length)

Truncated piles

The depth of truncation is given by

In this study, the soil material of the slope is simulated with an elastic, perfectly plastic model. The yielding is described by a composite Mohr–Coulomb criterion with a tension cutoff as shown in Figure

Composite Mohr–Coulomb failure criterion.

The failure envelope from points

The failure envelope from points

The truncated stabilizing piles are treated as a linear elastic solid material. Routines are developed to calculate the required parameters including the pile shear force and bending moment for the analyses. The shear force

Section of a horizontal pile representing parameters in an element.

The shear force

In this study, the interfaces between piles and soils are characterized by a linear Coulomb shear strength model. Interfaces have the properties of friction, cohesion, dilation, normal and shear stiffness, and tensile and shear bond strength. Figure

Components of the interface constitutive model.

The normal and shear forces that describe the elastic interface response are determined by the following equations:

In this study, where the use of interface element covers the pile-soil separation and nonlinear analysis is carried out, the value for the interface stiffness should be high enough to minimize the contribution of those elements to the accumulated displacements. A good rule-of-thumb is that ^{7} kPa/m in the current analyses. These values were also adopted by Comodromos and Papadopoulo [

For slopes,

The shear strength reduction method has two main advantages over limit equilibrium slope stability analyses. First, the critical slide surface is found automatically, and it is not necessary to specify the shape of the slide surface in advance. In general, the failure surface geometry for slopes is more complex than simple circles or segmented surfaces. Second, numerical methods automatically satisfy translational and rotational equilibrium, whereas not all limit equilibrium methods do satisfy equilibrium. Consequently, the shear strength reduction method usually determines the

To perform a slope stability analysis with the shear strength reduction method, simulations are run for a series of strength reduction factors

Figure

Numerical method for obtaining the FS of a truncated piled slope.

It should be noted that there are several possible definitions of failure, for example, some test of bulging of the slope profile, limiting of the shear stresses on the potential failure surface, or nonconvergence of the solution [^{−5}.

The proposed numerical method is executed with FLAC

The model is considered to be in equilibrium when the maximum unbalanced force for the whole grid is small in comparison with the total of the applied forces associated with boundary displacement or stress changes. Denoting

Idealized slopes with a height of 10 m, gradient of

3D finite difference mesh for Models

Model

Model

Truncated stabilizing piles with outer diameters

Schematic illustration of the analytical truncated piles.

Model

Model

It is well documented that the

Material properties.

Material properties | Pile | Soil | Weak layer |
---|---|---|---|

Unit weight (kN/m^{3}) | 25 | 20 | 20 |

Cohesion (kPa) | — | 10 | 7 |

Friction angle (°) | — | 20 | 14 |

Young’s modulus (MPa) | 60,000 | 200 | 100 |

Poisson’s ratio | 0.2 | 0.25 | 0.25 |

When the slopes are not reinforced with truncated piles, the

The critical slip surfaces for the two models are shown in Figure

Critical slip surface of unreinforced slopes for Models

Model

Model

The

Pile spacing | | |||||||
---|---|---|---|---|---|---|---|---|

0 | 0.18 | 0.35 | 0.53 | 0.71 | 0.88 | 1.06 | ||

| | 1.78 | 1.69 | 1.51 | 1.33 | 1.22 | 1.18 | 1.17 |

| 1.64 | 1.61 | 1.47 | 1.32 | 1.21 | 1.17 | 1.17 | |

| 1.57 | 1.54 | 1.44 | 1.32 | 1.21 | 1.17 | 1.17 | |

| 1.53 | 1.50 | 1.42 | 1.31 | 1.21 | 1.17 | 1.17 | |

| 1.49 | 1.47 | 1.41 | 1.31 | 1.21 | 1.17 | 1.17 | |

| 1.47 | 1.45 | 1.40 | 1.30 | 1.21 | 1.17 | 1.17 | |

| 1.44 | 1.44 | 1.38 | 1.30 | 1.21 | 1.17 | 1.17 | |

| ||||||||

| | 1.53 | 1.53 | 1.50 | 1.32 | 1.21 | 1.17 | 1.17 |

| 1.45 | 1.45 | 1.45 | 1.31 | 1.21 | 1.18 | 1.17 | |

| 1.41 | 1.41 | 1.41 | 1.31 | 1.22 | 1.18 | 1.17 | |

| 1.38 | 1.38 | 1.38 | 1.31 | 1.22 | 1.18 | 1.17 | |

| 1.36 | 1.36 | 1.36 | 1.31 | 1.21 | 1.18 | 1.17 | |

| 1.34 | 1.34 | 1.34 | 1.31 | 1.21 | 1.18 | 1.17 | |

| 1.33 | 1.33 | 1.33 | 1.31 | 1.21 | 1.18 | 1.17 | |

| ||||||||

| | 1.38 | 1.38 | 1.38 | 1.32 | 1.21 | 1.18 | 1.17 |

| 1.33 | 1.33 | 1.33 | 1.31 | 1.21 | 1.17 | 1.17 | |

| 1.31 | 1.31 | 1.31 | 1.30 | 1.21 | 1.17 | 1.17 | |

| 1.29 | 1.29 | 1.29 | 1.29 | 1.21 | 1.17 | 1.17 | |

| 1.28 | 1.28 | 1.28 | 1.28 | 1.21 | 1.17 | 1.17 | |

| 1.27 | 1.27 | 1.27 | 1.27 | 1.21 | 1.18 | 1.17 | |

| 1.26 | 1.26 | 1.26 | 1.26 | 1.21 | 1.18 | 1.17 |

The

FS values of the piled slopes for Model

It can be seen from Figure

For

For

For

It is demonstrated that the optimum value of the relative depth of truncation,

Variation of the

The bending moment

Truncated pile behavior characteristics for various pile spacing.

It can be seen from Figure

Depth of a potential slip surface at piles (units: m).

Relative depth of truncation | Pile spacing | ||||||
---|---|---|---|---|---|---|---|

| | | | | | | |

| 7.13 | 6.38 | 6.38 | 5.63 | 5.63 | 5.63 | 5.63 |

| 7.13 | 6.38 | 6.38 | 5.63 | 5.63 | 5.63 | 5.63 |

| 7.13 | 6.38 | 6.38 | 5.63 | 5.63 | 5.63 | 5.63 |

| 5.63 | 5.63 | 5.63 | 5.63 | 5.63 | 5.63 | 4.88 |

| 4.88 | 4.88 | 4.88 | 4.88 | 4.88 | 4.88 | 4.88 |

| 4.88 | 4.88 | 4.88 | 4.88 | 4.88 | 4.88 | 4.88 |

The values of the first extreme point of shear force

Variation of

It can also be seen from Figure

Failure mode of slopes stabilized with truncated piles (

Failure mode of a slope with piles

Through pile center line at

Through soil midway between piles at

Failure mode of a slope with piles

Through pile center line at

Through soil midway between piles at

Failure mode of a slope with piles

Through pile center line at

Through soil midway between piles at

Failure mode of a slope with piles

Through pile center line at

Through soil midway between piles at

Failure mode of a slope with piles

Through pile center line at

Through soil midway between piles at

Failure mode of a slope with piles

Through pile center line at

Through soil midway between piles at

Failure mode of a slope with piles

Through pile center line at

Through soil midway between piles

Model

The

FS values of the piled slopes for Model

It can be seen from Figure

For

For

For

Comparing

Failure mode of Model

Failure mode of piled slopes for Model

A novel engineering technique of truncated pile for slope stabilization was introduced in this paper. The truncated piles are more economical and rational than conventional full length piles due to their shortened length and smaller load.

A simplified numerical method was proposed to analyze the stability of slopes stabilized with truncated piles based on the shear strength reduction method, in which the soil behavior is described using the nonassociated Mohr-Coulomb criterion and a pile is modeled as 3D continuum elements. The reliability of the proposed method was tested using an example from Cai and Ugai [

The influential factors including pile diameter, pile spacing, depth of truncation, and existing a weak layer were systematically investigated by the proposed method from a practical point of view. It is found that an optimum ratio exists between depth of truncation and length of pile above critical slip surface. For the actual ratio is below the optimum value, the factor of safety of reinforced slope hardly changes with the pile truncation, indicating that truncation in this range has little influence on the reinforcement function of piles. Conversely, once the actual ratio is above the optimum value, truncation will play a serious influence on reinforced slope stability and the reinforcement function of piles will be much weakened. In practical engineering, piles could be truncated appropriately on the premise of ensuring the reinforcement function; thus resources could be saved and costs could be reduced. It is advised that borehole could be filled with surrounding soil and compacted in the standard procedure for the truncated part of piles.

The authors proposed an index,

The current 3D slope stability analysis is based on a simple homogeneous slope. However, the geometry of real slopes is more complex. For example, a natural slope often has curvature, and irregular surfaces appear in open-pit and roadside design. Besides, soil properties typically exhibit considerable variation from point to point even within nominally homogenous soil layers. Therefore, further research is required to consider the effect of complex geometries and material spatial variability.

The authors declare that they have no competing interests.

This work was supported by the Chinese National Science Fund (nos. 51574245 and 41002090) and the State Key Laboratory of Coal Resources and Safe Mining (China University of Mining and Technology) (no. SKLCRSM16KFB05).