i

ABSTRACT: This is the first in a series of two papers presenting a decoupled methodology for the design of slope stabilising piles. The proposed methodology combines the widely accepted analytical calculations to obtain the required stabilising force, with non-linear finite elements analysis to obtain the ultimate lateral capacity of piles. The soil and pile constitutive model is validated against experimental and observational data. The simplified numerical model results are compared satisfactorily with 3D Finite Elements analyses and theoretical studies.

1. INTRODUCTION

Landslides affect not only the structures founded on the slope, but also these ones lying in the area of soil mass deposition. Stabilisation measures most often refer to the strengthening of the interface. One of the most effective methods of this category is interface nailing using piles. Their use as a means of stabilization has been discussed, among others, by De Beer & Walleys, 1970; Ito and Matsui, 1975; Sommer, 1977; Fukuoka, 1977; D Appolonia et al. 1977; Wang et al, 1979; Nethero, 1982; Yamada et al, 1971; Fukumoto, 1972, 1973; itazima and Kishi, 1967; Leussink and Wenz, 1969; De Beer and Wallays, 1972; Nicu et al., 1971; Marche & Lacroix, 1972; eyman & Boersma, 1961; Heyman, 1965; De Beer et al., 1972; Tschebotarioff, 1973; to & Matsui, 1975; Hassiotis et al., 1997; Poulos, 1995; Chen & Poulos, 1993; Oakland & Chameaou, 1984; Goh et al., 1997; Poulos and Chen, 1997.

Most analysis methods are decoupled, i.e. they neglect the potential modification of the shape and position of the failure surface due to the very existence of piles. The pile is modeled as a flexural beam connected with the surrounding soil through non-linear springs. The soil displacement profile is transmitted to the beam through these non-linear springs. All analysis techniques necessarily include a number of simplifying assumptions regarding the springs. Moreover, the actual soil displacement profile is not straightforward to obtain; it must either be speculated or obtained by some sort of analysis (e.g. by means of finite elements) or by field measurements.

For this reason, this study attempts to propose an improved design methodology for slope stabilising piles which will maintain the simplicity of the most widely used methods but will simultaneously take advantage of rigorous finite elements calculation of the ultimate load of the soil-pile system incorporating all the complex non-linear phenomena discussed in the previous section (i.e. soil arching, soil-pile interaction and pile-pile interaction).

Piles for Stabilising Seismically Precarious Slopes. Part A : Development and Validation R. Kourkoulis, F. Gelagoti, I. Anastasopoulos, G. Gazetas Soil Mechanics Laboratory, National Technical University Athens, Greece

2. PROPOSED METHODOLOGY 2.1. Fundamentals of the Proposed Procedure The studied configuration is illustrated in Figure 1.A row of piles is embedded within the slope which is prone to failure. The upper soil layer, termed the unstable soil, overlies the stable soil layer. Inside the unstable layer lies the potential sliding interface. The main issue of the study is the estimation of the enhancement to stability offered by the piles.

Figure 1. Problem definition; a row of piles embedded within a slope which is prone to failure

The general design procedure follows the well documented decoupled approach described by

Viggiani (1981), Hull (1993) and Poulos (1995, 1999). It consists of two main steps :

1. Evaluation of the total shear force needed to increase the existing safety factor for the slope (based on an analysis without reinforcement) to the desired value.

2. Evaluation of the maximum shear force that each pile can provide to resist sliding of the potentially unstable portion of the slope without exceeding a preset design displacement limit; and selection of the type, number and most suitable location of the piles.

In the first step, the driving ( ) and the Resisting Forces ( )along the slip surface is

calculated utilizing one of the widely used slope stability analysis techniques (e.g. Sarma, Spencer, Bishop, Janbu). Most of these methods discretize the slope in slices and integrate the forces along each slice to obtain the total driving and resisting forces.

If the actual safety factor is less than the target safety factor , , the piles must provide and additional resistance , so that :

(1)

Hence, the required stabilizing force per unit width of soil that is to be provided by the piles may be calculated as:

(2)

For step (2), a reasonable procedure is to analyse the pile against lateral soil movements simulating the movement of a landsliding mass. Knowing the force per unit width that the piles, their properties and configuration may be obtained with 3 dimensional non-linear finite element analysis. Design charts can thus be developed to this end, for various soil and pile properties and pile configurations. Such a chart plots the Resisting Shear Force for the given soil conditions and landslide depth to decide upon the optimum pile configuration. Hence, the tedious procedure of designing the pile reinforcement is actually simplified to solving the slope stability equations.

The lateral capacity of the pile systems subjected to slope movements may be rigorously assessed utilizing the Finite Element technique which provides the ability to model the whole 3

dimensional geometry of the slope and pile system examined. Despite its rigor though, the analysis of the full model may be computationally ineffective because:

1. Pile loading, independently of the slope inclination and interface position is stemming from the application of a uniform displacement profile along the pile length. The reasonable validity of uniformity of the displacement distribution has been verified by Kourkoulis (2009) and is proposed by Poulos (1999) as very much appealing to the case of slope displacements.

2. Although the required pile resistance force is indeed a function of the slope geometry, its calculation has already been incorporated in the slope stability analysis described in Step (1). This decoupled approximation is totally realistic in case of pre-existing sliding planes within the soil mass.

3. Moreover, even if the slope geometry remains the same but the position of the interface (or of piles along the slope) has to be parametrically varied, a new model must be constructed and analysed each time, at enormous computational effort.

Therefore, in this section a more versatile simplified Finite Element Model is proposed that may be utilized for multiple parametric analyses. Despite the fact that the amount of induced loading on the pile is indeed a function of the slope inclination and interface properties, the ultimate load which is sought for at this stage is assumed to be a function of the interface position and soil properties only. Therefore, the model suitable for computing the pile ultimate load concentrates on the region around the pile. The validity of this demonstrated below..

3. NUMERICAL MODEL 3.1. Description The model is schematically displayed on Fig. 2, where the slope geometry has been eliminated. The position of the interface is defined by the depth of the unstable soil layer in the area around the pile. Therefore, the interface should be lying at depth from the free surface of the model.

The new model focuses on the region which is mostly affected by the pile. Therefore, for a pile of diameter D, the model dimension should be at least 10D, i.e 5D of soil behind and 5D of soil in front of the pile as shown in Fig. 2 (e.g. Reese and Van Impe, 2001).

Unlike the model length and depth which are determined by the slope geometry, the model width is a function of the piles spacing. The FE model represents a typical slice of the slope stabilized with piles spaced at distance S, which is assumed to be repeated infinitely in the y-direction. Consequently the width of the model is equal to 2S. [Pile center-to-center spacing: s, distance of each pile from the nearest side 0.5 s, i.e. model total of 2s]. The displacement is applied following a non-linear increase from zero to an ultimate value. The maximum value of the imposed displacement must be sufficient to mobilize the full resistance of the pile-soil system. A uniform displacement profile is applied in accord with several other researchers.

3.2. Soil and Pile Constitutive Modelling The soil is assumed to obey an elastoplastic constitutive model with Mohr-Coulomb failure criterion. The bottom stratum is considered to be rock and is therefore modelled as a stiff elastic material. The overlying soil layers are assigned the properties of the soil being modelled in each case. A row of hexahedral elements of reduced strength (residual strength parameters) models the sliding interface.

As schematically illustrated in Fig. 3 the pile is modeled as a 3D beam element is circumscribed by 8-noded hexahedral solid elements. The central beam element node is connected with the circumferential solid element nodes at the same height through appropriate kinematic restraints. The surrounding elements have zero rigidity : their presence only aims at capturing the solid geometry of contact between soil and pile.

Both elastic and inelastic piles are modeled. For the latter case, the moment-curvature relation, , of the pile cross-section is required, which initial depends (for reinforced-concrete piles) on the amount of reinforcement. An example is given in Fig.3.

Figure 2. Schematic Representation of the proposed versatile model for assessing the Pile lateral capacity.

Figure 3. Schematic Representation of the proposed versatile model for assessing pile lateral capacity.

3D8nodedhexahedralsolidElements,E=0

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4.3. Comparison with 3D Finite Element Model Results The finite element model is depicted in Figure 6. In the original case, the interface properties changed seasonally, resulting to soil movements and pile deformation. In the Finite Element analysis presented here, the shear strength of the interface is assumed to be reducing until the onset of failure. This is achieved through a user subroutine encoded in ABAQUS which defines the strength reduction pattern. The deadman anchor force was modelled as an induced concentrated force on the pile head. The data provided by the author have been utilized to model the sequence of : (a) pile loading , (b) pile head deflection, and (c) anchor pull-back.

Figure 7. Finite Element Model utilized for the simulation of the Salldes case study and detail of the mesh near the pile.

Figure 8. Pile displacements before (left figure) and after (right figure) the pulling-back operation of November 1986 (upper figure), September 1992 (middle figure) and July 1995 (bottom figure). Black line denotes the numerical analysis results while the field measurements of Frank & Pouget are denoted with the gray markers.

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The Finite Element analysis was performed in several steps. An initial run (artificial reduction of the shear strength along the interface) was performed (without the pile) to compute the time history of free field soil displacement (Figure 7).

To model the seasonal variation of the slip surface strength, the strength reduction pattern has been calibrated accordingly. The anchor force vs soil displacement can be converted to anchor force time history (where the time is measured in analysis step time and not real time). This loading history is applied on the pile head in the second run of the analysis.

During this second run, the analysis is repeated, but with the pile installed in its place. The produced pile deflection line before and after each anchor pulling is plotted in Figure8 at various stages of the anchor pull-back, compared with the Frank & Pouget (2008) measurements. It is observed that the model accuracy in the prediction of the slope and pile displacements is remarkable, enhancing the confidence in the proposed modelling technique.

5. VALIDATION OF THE SIMPLIFIED NUMERICAL MODEL

5.1. Validation Against Rigorous 3D FE Analyses The proposed simplified procedure is validated via comparisons with the 3-D finite element model. We assume a slope of the geometry and soil properties displayed in Fig. 9. The top layer is assumed to be a relatively loose sandy soil with 28 , 3 , and 2 . The bottom layer is assumed to be soft rock with 600 . A predefined sliding interface (highlighted in blue in Fig. 9) is assumed of residual strength : 16 , 3 , and

1 .

5.2. Slope Stability Analysis : Calculation of Required Pile Shear Force Utilizing the simplified Bishops method, the sum of the driving forces is 1936 / , while the sum of the resisting forces is calculated to be 1744 / . Hence the slope is characterized as unstable. The analysis seeks for the extra resistance force that must be obtained by the piles for the safety factor to become unity, i.e the pile force must be: 192 / .

Figure 9. The Full 3D Finite Element model. The pre-defined slip surface is highlighted in blue.

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5.3. Full 3 Finite Elements Analysis An initial analysis of the 3D model is performed in free field conditions, (i.e. without any piles). A snapshot of the deformed mesh at the end of the analysis is portrayed on Figure 10(a). The unstable soil clearly slides along the slip surface. Failure is confirmed by the increasing nodal velocity of elements on the sliding soil mass indicated on the time history plotted on Figure10(b).

In the next step, the analysis is repeated with the presence of reinforced concrete piles of diameter 1.2 spaced at 3 are used to stabilize the slope. For the example geometry under consideration the depth of the unstable soil is 8 . The results of the fully non-linear FE analysis are displayed in terms of horizontal displacement contours on Figure 11(a). It is evident that the chosen pile configuration able to prevent slope failure. The time history of the pile head displacement is portrayed in Figure 12. Note that the ultimate pile head displacement is up=2 cm.

5.4. Comparison between the 3D and the proposed simplified FE model The simplified model utilized for the assessment of the piles lateral capacity for the case examined is shown in Figure 13. The model is imposed to a horizontal displacement . The plot of the net resistance force against pile head displacement is displayed on Figure 14. For pile head displacement 2. (which corresponds to the pile deformation necessary to impede the landslide calculated by the fully 3D FE analysis), the corresponding resistance force calculated by this model is 173 / , which is almost practically equal to the one calculated through slope stability analysis.

Figure 10. Snapshot of the deformed mesh in the free-field case (upper figure) and plot of displacements time history of 2 nodes on the ground surface (bottom figure).

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5.5. Validation Against Theoretical Studies Poulos (1995) suggests that for the calculation of the ultimate lateral pressure developed on a pile by flowing sand, the simplest approach is to utilize the formula proposed by Broms (1964), in which:

(3)

is the Rankine passive pressure coefficient which is defined as

45 (4)

Where : is the angle of internal friction of soil ; is the effective overburden pressure ;and is a coefficient ranging between 3 and 5.

For clayey soils, total stress approach is usually adopted, in which is related to the undrained shear strength as follows :

(5)

where is the lateral capacity factor.

The lateral pile capacity can be calculated by means of the finite elements method utilizing the decoupled design approach presented in the previous sections. The plot of Resistance Force developed per pile (and not per unit width) versus soil free-field displacement for the case of a shallow landslide in sand stabilized by piles is displayed in Figure 15. for three cases of pile spacings. The ultimate value ( ) of the Resistance Force is clearly indicated by the curve flattening (displacements keep increasing while the resistance force remains constant). The ultimate lateral soil pressure calculated according to the Broms (1964) formula is:

3 45 (6)

And therefore the theoretically calculated ultimate pile resistance force is approximately:

3 45 (7)

for z = 6m and D=1.2 RF is equal to 3590 kN The value of the ultimate pile resistance force calculated by the numerical analysis for the

three cases is: 4 : = 3650 kN For pile spacing

3 : = 3100 kN For pile spacing

2 : = 2200 kN For pile spacing

It can be seen that the calculated values for the case of closely spaced piles deviate substantially from the Broms 1964 approach. This is due to the group interaction effect caused by neighboring piles.

6. CONCLUSION In this paper, an improved methodology has been presented and validated for the design of slope stabilising piles. The calculation of the pile ultimate lateral capacity is achieved by means of 3 dimensional finite elements analyses. The comparison of numerical model predictions with analytical, theoretical and field data reveals very good. The methodology presented herein is used in the second (companion) paper to contact a detailed parametric analysis, and derive deeper insight, on the performance of slope stabilizing pile.

Figure 11 (a). Contours of horizontal displacements when piles of 1.2m diameter are installed with 3D pile to pile distance.

Figure 11 (b). Zoom-in in the pile area. Note that the model can capture the 3-d displacement pattern around the piles.

Figure 12. Displacement time history at the head of the slope stabilizing pile

1.2mdiameter pilesspacedat3D

6D

8 m

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0 1 2 3 4 5 6 7

t (sec)

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upmax =2cm

Figure 13. The Simplified Finite Element Model utilized for the design of the stabilization piles of the previously described case study.

Figure 14. Pile resistance Force against pile head displacement. Case study: Pile spacing at 3D, landslide depth 8m, unstable soil properties = 28, c=3 kPa.

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Interface

=28 , c=3 kPa , =2Unstable soil

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/m

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Type HOM, linear PileType HOM, linear Pile

atup =2cm up (cm)

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)

176kN/m

Pilespacing3D

700

Figure 15. Resistance Force Developed on each pile as a function of the free field displacement and pile spacing.

ACKNOWLEDGEMENT The research presented in this paper was financially supported by the Secretariat for Research and Technology of Greece, under the auspices of PENED Programme with Contract number 03ED278.

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uff : cm

2D3D4D

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