Different aspects regarding slope stability improvement using piles

The problem of slope stability is a common one in the field of geotechnical engineering. There is more than one method that can be adopted in order to improve the stability of a slope. During the last decade, using piles for improving the mechanical behaviour of slopes has become the main approach of dealing with unstable slopes. In the current paper, the stability of a slope was analysed by using the tridimensional finite elements method using different scenarios of consolidation with timber piles. A parametric analysis was carried out for two different slopes: sand slope and soft soil slope. There were also analysed two different constitutive models: Mohr-Coulomb and Hardening Soil Small with different location of the consolidation system. The stability analyses employed both timber piles and concrete piles which were modelled in Plaxis 3D software by using two different approaches: embedded piles and volume piles. In the end, the most favourable position for the pile consolidation system is highlighted in order to attain the maximum stability of the slope. Also, different aspects of the constitutive models, modelling the piles and pile material are discussed from the point of view of slope stability improvement.


Introduction
Landslides are natural phenomena that can occur in both natural or anthropic slopes.In some cases, they can result in material and property damage, or even in loss of human lives [1].The problem of soil movement can be partially or totally resolved by slope stabilizing techniques which aim to increase slope stability and safety of the dangerous sites.In the recent decades, one of the most used method for achieving such results is using piles in order to consolidate the slopes that are suspected to become unstable [2], [3].The benefit of using such a system can be quantified by using different methods of slope stability analysis, such as limit equilibrium methods (LEM), bidimensional finite elements methods (2D FEM) or tridimensional finite elements methods (3D FEM).All types of approaches have advantages and disadvantages, but it was showed that using a 3D method gives more insight into the complex task of modelling the real behaviour of a slope consolidated with piles [4].Introducing piles inside the soil domain of analysis considerably increases the difficulty of the problem, as it opens the door for other important aspects such as: interaction between the piles and the soil, slope geometry, piles position, the modelling approach of the piles, constitutive model adopted and so on.
Another important aspect would be the impact of such a system on the environment and its ability to be sustainable.As nowadays most of the geotechnical structures are made out of reinforced concrete (which has a great equivalent CO2 footprint), piles made out of wood could be an alternative to alleviate these disadvantages.
In these regards, in the current paper timber piles are analysed in comparison with concrete piles in order to evaluate the differences in behaviour and the possibility of using timber piles for slope stability improvement.The modelling of piles and soil was also approached through different ways.The soil was modelled by both Mohr-Coulomb (MC) model and Hardening Soil Small (HSS) model.The piles were modelled by using the embedded pile approach and the volumetric approach (volume piles), both options being available in the Plaxis 3D software.

Geometric and geotechnical characteristics of the analysed slopes
In order to apply all the aspects described above, a slope geometry was adopted.The geometry is shown in figure 1 and consisted in two different homogeneous configurations: sand and soft soil.Taking into account that the optimum location of the piles was analysed, 12 possible locations of the row of piles were involved, ranging throughout the entire length of the slope, as shown in figure 2. Also, the length of the slope profile was considered being equal with Lprofile=20.00m during the analyses using embedded beams and Lprofile=3.40 m during the analyses using volume piles.All the piles that were modelled in the stability analyses (timber or concrete) were given the same geometrical characteristics, according to table 5. Regarding the modelling of the soil slope using the Plaxis 3D software, the dimension of the finite elements was chosen as "fine" according to the software settings in order to reach equilibrium between the accuracy of the results and the analysis duration.

Different aspects regarding the constitutive models and modelling of piles
In numerical analyses, the behaviour of a soil mass can be greatly influenced by the adopted constitutive model for the soil.In order to compare the results, all the stability analyses that were carried out in this paper were done by employing both Mohr-Coulomb and Hardening Soil Small model.
The Mohr-Coulomb model is an elastic perfectly-plastic model that requires only 5 geotechnical parameters (see table 1 and table 2).Determining these parameters can be done either on site or in the laboratory.The basic idea behind the elasto-plastic modelling of the soil is that the strains are divided into the elastic and plastic ones.In order to corelate the state of stress with the elastic strains, Hooke's law is used.According to plasticity theory, the deformation state is proportional with the first order derivative of the plasticity function divided by the derivative of the stresses.Also, a plastic potential function is introduced, in order not to overestimate the dilatancy phenomenon.Being a first order model, it is usually used for general modelling of soil, dam stability analysis, slope stability and is not recommended for modelling clays or soft soils due to overestimation of the rigidity of normally and under consolidated soils [6].
On the other hand, the more advanced models which take into account the increase in rigidity at small strains may prove to be advantageous in closely modelling the soil-structure interaction.One of these models is Hardening Soil Small model, which represents an extension to the base model Hardening Soil integrated in Plaxis software.
The HSS model tries to model basic phenomena that take place in the soil mass, such as: increase in density, dependency of the rigidity on the stress levels, creep, dilatancy and rigidity variation depending on the tangential strains.The Hardening Soil Small model is one of the simplest small strain models which uses almost the same geotechnical parameters as Hardening Soil model (see table 4 and table 5).HSS model is usually adopted in deformation problems during the analysis of retaining walls, retaining geotechnical structures, etc. with almost no evidence of being used in slope stability problems.
Regarding the modelling of the piles, Plaxis 3D offers two alternatives of doing it: embedded piles or volume piles.
Embedded piles are elements that after discretization become linear elements having 3 nodes, each with 6 degrees of freedom.During a slope stability analysis, the piles from the slope body will be loaded by lateral forces.From this point of view, embedded pile elements have some limitations: being linear elements they cannot overlap and the soil-structure interaction is ensured by introducing slide elements in the axial direction of the elements.Unfortunately, slide elements cannot be introduced on the horizontal direction and the piles do not take into consideration the friction between them and the soil when they are laterally loaded.Even though this aspect is important for consolidation piles, acceptable behaviour of embedded piles is demonstrated in the literature [7].The advantages of embedded piles are visible when there is a great number of piles that needs to be modelled, as the computational time is much more decreased than for using same amount of volume piles.
On the other hand, volume piles are elements that allow a 1:1 representation of a pile in the tridimensional space.The most important aspect is that the interface between the soil and the elements can be modelled through specific surface elements.The contact between different types of surfaces is simulated by affecting the strength at the interface level through the reducing factor R inter.For the current paper, different types of contacts were analysed: sand-wood, soft soil-wood, sand-concrete, soft soil-concrete, for which the values of Rinter were chosen according to [8] (table 6).
After the discretization of the domain, the volume piles will be a part of the mesh, the dimensions of the finite elements will be restricted to smaller values.Even though this aspect may increase the accuracy, it will also significantly increase the computation time which is a major disadvantage of this type of element.
Regarding the degree of freedom of the piles heads, all the piles modelled in the current paper were considered having free head.This is the most detrimental situation for the pile head fixity which will generate the smallest value for the factor of stability.

Parametric analysis of the optimal piles position with embedded pile modelling
The first parametric analysis comprised finding the optimal position of the pile consolidation system.All the slope stability analyses were conducted by adopting both constitutive models discussed above (MC and HSS) and both types of piles: timber and concrete piles.While the geometrical characteristics of the piles were the same, the material properties of the piles were chosen according to table 7 and table 8 depending on the pile material.All the piles in this analysis were modelled only by using embedded beam elements.The variation of the safety factor (Fs) in relation to the position of piles for different constitutive models and pile material is presented in figure 3 for the sand slope and in figure 4 for the soft soil slope.
As it can be seen in figure 3 for the sand slope, the values of Fs are varying depending on the position of the piles and on the adopted constitutive model.
For the timber piles where the soil was modelled using Mohr-Coulomb model, the highest values of the stability factor were registered on the positions 6 and 8, approximately representing the middle of the slope.Considering the value of Fs obtained for the unreinforced slope, in the case of timber piles modelled with MC model, only three locations of the piles generated greater values: 6, 7 and 8.The analyses showed that when the timber piles are placed on other locations, the stability of the slope is decreased and therefore the chosen solution is not suitable.The results obtained by using the HSS model show a similar variation for the factor of stability, but with smaller differences between the smallest and the greatest values.In this combination of factors, the greatest value for Fs was generated on position no.7, being the only location where the factor of safety has a greater value than the factor of safety of the unreinforced slope.
Taking into consideration the behaviour of the concrete piles for the same sand slope, the variation of Fs is similar to the one obtained for the timber piles.In this case, only two positions of the piles generated Fs values greater than the ones for the unreinforced slope and those are positions no.6 and 7 (approximately the middle of the slope).This result is valid for both constitutive models employed.On all the other locations, placing the concrete piles will result in a decreasing stability factor and therefore other consolidation solutions may prove efficient.Comparing the results generated by the two constitutive models regarding the sandy slope, it can be observed that the results follow more or less a similar variation.Looking at the smallest values for Fs both models generated very close values with the greater difference being in comparing the largest values of the stability factor.In this case it can be considered that Mohr-Coulomb model sensibly overestimates the values of Fs, but the general behaviour is very similar.
For the soft soil slope, figure 4 shows that the variation of the factor of stability with the position of the piles can almost be approximated by a constant variation.The values of Fs for the unreinforced slope are almost equal for MC and HSS models, which is showed by the overlapping horizontal lines in figure 4. It can also be observed that almost all values of the factor of stability are superior to those generated by the unreinforced slope (except position no. 1 for timber and concrete piles modelled with MC model).This means that the consolidation with piles is beneficial for the soft soil slope regardless of the position.The maximum values of the stability factor were obtained on the 2 nd position for timber piles with MC model, on 3 rd position for timber piles with HSS model and on 3 rd position for concrete piles with both constitutive models which indicates the optimal position of the system in the lower third of the slope.
From the constitutive model point of view, the values generated by Mohr-Coulomb model and Hardening Soil Small model are very similar and the differences are neglectable, which means that both models are appropriate for the analysis of the stability level of a clay slope.Comparing the behaviour of timber and concrete piles, the values of Fs are seemingly not affected by the material of the piles.In these regards, a consolidation with timber piles could be feasible from the stability point of view.

Parametric analysis of the optimal piles position with volume pile modelling
Volume pile elements represent a way to accurately model a pile in a tridimensional environment.Using this approach requires the user to model the piles by using the real dimensions of the elements and therefore volume piles can better simulate the interaction between the piles and the soil.
To investigate the influence of a pile consolidation system modelled with volume piles on the stability of a slope, a parametric analysis was carried out.The geometric characteristics of the slope are the same as in the previous analysis and it was considered a homogeneous slope made of sand and soft soil with the geotechnical characteristics according to table 1 and table 2 for Mohr-Coulomb model and according to table 3 and table 4 for Hardening Soil Small model.The geometrical characteristics of the piles were kept the same and the material was timber and concrete respectively.
Taking into account the disadvantages of modelling piles as volume piles, the length of the slope profile was set to a smaller value (4.00 m) in order for the analysis to comprise only 3 piles.This modification lead to decreased analysis time which allowed more analyses to be conducted in a shorter amount of time.Another aspect is that only position 1, 6, and 11 were analysed, representing the bottom, middle and the top of the slope.This alteration was made also due to the increased time of analysis required when using volume piles.The results are presented in figure 5 and figure 6.The variation of Fs which is showed in figure 5 for the three positions studied, expresses the fact that in the case of the sand slope, the optimal location of placing the piles is somewhere at the middle of the slope.This result is generated by both MC and HSS constitutive models.Also, even though the values of the factor of safety are not the same, they can be considered sensibly close for timber and concrete piles respectively.
It can be observed form figure 5 that for position no.6, all the values of Fs are greater than those obtained for the unreinforced slope, while on the positions no. 1 and 11, the values of the stability factor for the consolidated slope are smaller or equal with those of the unreinforced slope.This signifies the fact that placing a consolidation system at the bottom or the top of the sandy slope would not have a beneficial effect on the stability of the slope, therefore they are not economical.
Analysing figure 6 which shows the values of the stability factor for the soft soil slope, it can be seen that all of them are greater than the values of Fs for the unreinforced slopes.This makes the consolidation system worthwhile for the stability of the slope, regardless the position of the piles.The optimal location for the consolidation system is, according to figure 6, at the bottom of the slope.This observation can be made for all the studied cases with the exception of the concrete piles analysed with Mohr-Coulomb model.For this case, the smallest value of Fs was generated at the bottom of the slope and for the other two positions, the variation was constant (same value of Fs).All the results obtained in the numerical analyses by modelling the piles as volume piles for both types of slope (sand and soft soil) follow the same trend as the ones generated by the embedded piles analyses.Even though the magnitude of the values is different, the results show that for a sandy slope, the consolidation system is more efficient if it is placed somewhere at the middle of the slope while for a soft soil slope, the system should be placed somewhere at the bottom of the slope (lower third of the slope) for maximum stabilisation effect.In figure 7 and figure 8, the results obtained by using volume piles (VP) were plotted against those obtained by using embedded piles (EP).It can be observed that in the case of sandy slope, embedded piles were more conservative and should be used in these types of situations in order to be on the safe side.On the other hand, the soft soil slope volume piles solution gave the most pessimistic result and represents the safer way of approaching the pile modelling.

Conclusions
The current paper presents the results obtained from several parametric analyses which involved the stability computation for two homogeneous slopes (sand and soft soil), by employing different constitutive models (Mohr-Coulomb and Hardening Soil Small), for different types of piles (timber and concrete) which were modelled by using two different methods available in Plaxis 3D software (embedded piles and volume piles).The conclusions that were reached are the following: • The optimal position of the pile consolidation system depends on the type of soil in the slope body.For slopes made of sand, the best placement of the system would be at the middle of the slope and for slopes made of soft soil, in the lower third according to the numerical analyses presented.It was also observed that sandy slopes are more sensible to a consolidation system with some generated values for F s being smaller than those of the unreinforced slope.• From the stability point of view, the difference between Mohr-Coulomb model and Hardening Soil Small model is not very dramatic.The most important difference lies in the number of parameters required in order to apply the two models.As MC model needs less parameters, which are more easily available than those for the HSS model, it is the recommended constitutive model to be used in routine stability analyses, which is in accordance with the literature.• The behaviour of timber and concrete piles was also analysed.It was shown that, from the stability point of view, the behaviour is very similar and timber piles could be a more sustainable alternative which benefits from the low equivalent CO2 footprint.• The method of modelling the piles in the 3D domain can have an impact on the behaviour of the consolidation system.Even though the volume piles represent the more accurate way of modelling the piles, they are limited by the very increased time necessary for the numerical analysis and the dimension of the finite elements.It was observed that for models containing more than three volume piles, the necessary analysis time can increase with as much as 3 to 4 times than the same situation modelled using embedded piles.It was also shown that for sandy slopes embedded piles generated more conservative results and should therefore be used, while for soft soil slopes the volume piles generated the most pessimistic result and should be used in such situations.

Figure 1 .
Figure 1.Profile of the analysed slope.

Figure 2 .
Figure 2. Possible positions of the piles analysed.

Figure 3 .
Figure 3. Variation of Fs depending on embedded piles position for a slope made of sand

Figure 4 .
Figure 4. Variation of Fs depending on embedded piles position for a slope made of soft soil

7 Figure 5 .Figure 6 .
Figure 5. Variation of Fs depending on volume piles position for a slope made of sand

Figure 7 .Figure 8 .
Figure 7. Variation of Fs depending on piles position for a slope made of sand

Table 1 .
Geotechnical parameters for sand in MC model.

Table 2 .
Geotechnical parameters for soft soil in MC model.

Table 3 .
Geotechnical parameters for sand in HSS model.

Table 4 .
[5]technical parameters for soft soil in HSS model.The geotechnical characteristics for each type of soil were chosen according to H. F. Schweiger[5]for both Mohr-Coulomb and Hardening Soil Small models and are presented in table 1, table 2, table 3 and

Table 5 .
Geometrical characteristics of the modelled piles.

Table 6 .
Values of Rinter factor depending on different types of materials.

Table 7 .
Material properties of wooden piles for 12% moisture content.

Table 8 .
Material properties of concrete piles for C25/30 class concrete