canadian piles

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Design of reinforcing piles to in s slope stability Harry 6. Poulos

Abstract: This paper describes an approach for the design of piles to reinforce slopes, involving three main steps: (1) evaluating the shear force needed to increase the safety factor to the desired value; (2) evaluating the maximum shear force that each pile can provide to resist sliding of the potentially unstable portion of the slope; and (3) selection of the type and number of piles, and the most suitable location of these piles within the slope. For step 1, stability analyses can be used to assess the required additional shear force for stability. Step 2 involves the use of a computer analysis for the response of a pile to laterally moving soil. This analysis can be implemented via a computer program ERCAP, and enables the resisting shear force developed by the piles to be evaluated as a function of pile diameter and flexibility and the relative depth of the soil movement in relation to the pile length. Step (3) involves the use of engineering judgement in conjunction with the analysis results from steps 1 and 2. The paper describes the ERCAP analysis and the characteristics of pile behaviour it reveals. The application of the approach to a highway bypass problem in Newcastle, Australia, is described in detail. In the final design, a total of 64 bored piles 1.2 m in diameter were used over a total length of slope cutting of about 250 m. The pile lengths ranged between 6 and 12 m, with the spacings varying between 3.2 and 6.0 m.

Key words: analysis, boundary element, piles, soil-pile interaction, slope stabilization, soil mechanics.

RCsumC : Cet article prCsente une approche de calcul de renforcement de pentes par des pieux selon trois Ctapes principales : (1) Cvaluation de la force de cisaillement nCcessaire pour amener le coefficient de sCcuritC ?i la valeur dCsirCe; (2) evaluation de la force de cisaillement maximum que chaque pieu peut fournir pour rCsister au glissement de la section Cventuellement instable de la pente; (3) choix du type, du nombre de pieux et de la position la plus judicieuse de ces pieux le long de la pente. Pour 1'Ctape I on peut utiliser des analyses de stabilitC pour apprCcier la force de cisaillement additionnelle nCcessaire B la stabilitC. L'Ctape 2 implique l'utilisation d'un ordinateur pour analyser la rCponse d'un pieu B un mouvement latCral du sol. Cette analyse peut &tre faite grhce au programme ERCAP et elle permet d'Cvaluer la rCsistance au cisaillement dCveloppCe par les pieux en fonction de leur diamktre et de leur flexibilitC ainsi que la profondeur relative du mouvement du sol par rapport B la longueur du pieu. L'Ctape 3 fait appel au jugement de I'ingCnieur et s'appuie sur les rCsultats des analyses des Ctapes 1 et 2. L'article decrit l'analyse par ERCAP et les aspects du comportement des pieux qu'elle rCvble. L'application de cette approche ?I un problkme de route de dktournement B Newcastle, Australie, est prCsentCe en detail. Dans la conception finale, on a utilisC un total de 64 pieux forks de 1.2 m de diamktre, sur une longueur totale d'escarpement de pente d'environ 250 m. La longueur des pieux Ctait comprise entre 6 et 12 m, avec un espacement variant entre 3.2 et 6.0 m.

Mots clPs : analyse, Clement frontikre, pieux, interaction sol-pieu, stabilisation de pente, mCcanique des sols.

[Traduit par la rgdaction]

Introduction

One method that has been used to improve the stability of slopes has been via the installation of piles. The suc- cessful use of this method has been described by several

I Received November 4, 1994. Accepted May 1, 1995.

H.G. Poulos. Coffey Partners International Pty. Ltd., 12 Waterloo Road, North Ryde, NSW 21 13, Australia, and School of Civil and Mining Engineering, The University of Sydney, Sydney, NSW 2006, Australia.

investigators (for example, Sommer 1977; Esu and D'Elia 1974; Ito and Matsui 1975; Ito et al. 1982; Nethero 1982; Morgenstern 1982; Gudehus and Schwarz 1985; Reese et al. 1992; Rollins and Rollins 1992). Despite these appli- cations, the methods used for the design of the stabilizing piles vary widely, and some of the methods appear to be of doubtful validity.

The purpose of this paper is to set out a relatively simple framework for the design of the slope-stabilizing piles, and to describe an analysis which may be used to quan- tify the response of piles to soil movements arising from

Can. Geotech. J. 32: 808-818 (1995). Printed in Canada I Irnprirnt au Canada

Poulos

Fig. 1. Model for piles in soil undergoing lateral movement.

(a) Stresses, forces, and (b) Stresses on (c) Suecified horizontal moments on pile soil

slope instability. Estimation of the necessary geotechnical parameters is then discussed, and finally application of the design approach to the stabilization of a highway cutting in Newcastle, Australia, is described.

Design procedure for stabilizing piles

The general design approach adopted follows closely that described by Viggiani (1981) and involves three main steps: (1) evaluating the total shear force needed to increase the safety factor for the slope to the desired value; (2) evaluating the maximum shear force that each pile can provide to resist sliding of the potentially unstable portion of the slope; and (3) selecting the type and number of piles, and the most suitable location in the slope.

Step 1 makes use of the detailed results of the stability analysis. The actual safety factor F V o r a slope can be defined as follows:

where CR is the sum of resisting forces along the critical failure surface; and SF, is the sum of disturbing forces along that surface.

If the actual safety factor Fa is less than the target safety factor, FT, the piles must provide an additional resistance AR, so that

CR+AR 121 FT =------

C F i From eqs. 1 and 2,

This represents the stabilizing force, per unit width of soil,

mbvement of soil

that must be provided by 1hedpiles and can readily be cal- culated if CFD is 'extracted from the stability analysis results.

For step 2, the most satisfactory procedure is to under- take an analysis in which the pile is subjected to soil movements that simulate the movement of a sliding mass of soil over a stable mass.

I t should be noted that the safety factor can also be defined in terms of moments along the failure surface, rather than only the forces, e.g., NAVFAC (1986). The principle of the method is the same, regardless of the def- inition of the safety factor.

Viggiani (1981) has derived dimensionless solutions for the ultimate lateral resistance of a pile in a two-layer purely cohesive soil profile. These solutions, while being extremely valuable, are limited in the following respects: ( i) they apply only to purely cohesive soils in which cohesion of the unstable and stable soil is assumed constant with depth; (ii) they apply to the ultimate state only and do not give any indication of the development of pile resistance with soil movement; and (iii) they are confined to a simplified rep- resentation of the distribution of soil movement with depth.

A somewhat more versatile approach, which enables the above limitations to be overcome, can be developed by using a pile-soil interaction analysis in which the effect of soil moving past the pile can be considered. Such an analysis has been described by Poulos (1973), Poulos and Davis (1980), and Lee et al. (1991) and makes use of a simplified form of boundary element analysis to obtain a solution. A brief description of this analysis is given in the following section.

Guidelines for step 3, and in particular the optimal location of piles in a slope, are not well-established. However, it is clear that, in order to be effective, stabilizing piles must have the following characteristics: ( i ) they must be of

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i , Can. beotech. J. Vol. 32, 1995

\ Fig. 2. Basic problem of a pile in unstable slope: free-field soil movement.

Unstable soil

Stable soil

I Stable zone

relatively large diameter and relatively stiff; so that a rea- sonably large stabilizing force can be generated without causing failure of the pile; (ii) they must extend well below the critical failure surface so that the failure surface is not merely shifted downwards below the pile tips with a factor of safety still less than the target value; and (iii) they should be located in the vicinity of the centre of the critical failure circle (or wedge, etc.) to avoid merely relo- cating the failure surface behind, or in front of, the piles.

Method of analysis of pile resistance

The lateral response analysis used herein relies on the use of a simplified boundary element analysis. In this case, the pile is modelled as a simple elastic beam, and the soil as an elastic continuum. The basic problem is illustrated in Fig. 1. The lateral displacement of each element of the pile can be related to the pile bending stiffness and the horizontal pile-soil interaction stresses. The lateral displacements of the corresponding soil elements are related to soil modulus or stiffness, pile-soil interaction stresses, and free-field horizontal soil movements. A limiting lateral pile-soil stress can be specified so that local failure of the soil can be allowed for, thus allowing nonlinear response to be obtained.

By consideration of the compatibility of the horizontal movements of the pile and soil at each element, the following equation may be derived if conditions at the pile-soil interface remain elastic:

[I]-' [41 [[Dl+ 51 (AP} = -h KRtz {Ape)

where [Dl is the matrix of finite difference coefficients for pile bending; [I]-' is the inverted matrix of soil displacement factors; K, is dimensionless pile flexibility factor = EIIE,L~;

Assumed Distribution of Lateral Soil Movement

n is the number of elements into which pile is divided; { A p } is incremental lateral pile displacements; {Ap,} is incremental free-field lateral soil movement; EI is the bending stiffness of pile; E, is average Young's modulus of soil along pile shaft; and L is embedded length of pile.

In addition, the horizontal and moment equilibrium equations, and the pile head and tip boundary conditions, may be expressed in terms of displacements. After solving the resulting equations for incremental displacements, incremental pressures may then be evaluated from the equation of bending of the pile and added to the existing pressures to obtain the overall pile-soil pressures. These values are compared with the specified limiting lateral pressures, and at those elements where the computed pressure exceeds the limiting value, the compatibility equation for that element is replaced by the pile bending equation, which incorporates the condition that the lateral pressure increment is zero. The solution is then iterated until the computed lateral pressures nowhere exceed the limiting values. A FORTRAN 77 computer program, ERCAP (Earth Retaining Capacity of Piles), has been developed to imple- ment this analysis. ERCAP is a proprietary program, but some details of the theoretical analysis, coding, and data requirements are given in CPI (1992).

The lateral response analysis requires a knowledge of the distributions of lateral soil modulus and limiting lateral pile-soil pressure with depth, and the free-field horizontal soil movements. For problems involving slope instability, a distribution of free-field soil movements such as that shown in Fig. 2 appears to be appropriate. This assumes that a large volume of soil (the upper portion) moves as a rigid body downslope. Below this is a relatively thin zone undergoing intense shearing in the "drag zone." The underly- ing "stable zone" is stationary. The estimation of lateral soil modulus and limiting lateral pile-soil pressure will be discussed later in this paper.

Poulos

Some observations from the theoretical analysis

Analyses employing ERCAP have revealed the existence of the following modes of failure: (i) the "flow mode," when the slide is shallow and the unstable soil becomes plastic and flows around the pile; (ii) the "short-pile mode," when the slide is relatively deep and the length of pile in the stable soil is relatively shallow; the sliding soil carries the pile through the stable soil layer and full mobilization of soil strength in the stable layer occurs; (iii) the "intermediate mode," when soil strength in both the unstable and stable soil is fully mobilized along the pile length; and (iv) "long- pile failure," which occurs when the pile itself yields because the maximum bending moment reaches the yield moment of the pile section; this mode can be associated with any of the three modes of soil failure above, although experience suggests that it is most likely to occur with the intermediate mode.

Figure 3 illustrates characteristics of pile behaviour for the flow mode, the short-pile mode, and the intermediate mode. The results are for a 15 m long steel tube pile with an external diameter of 0.5 m and a wall thickness of 15 mm. In the upper sliding zone, the soil is a clay with an undrained shear strength of 30 kPa, while in the lower "stable" zone, the undrained shear strength is 60 kPa. The soil movement in the slide zone is assumed to be constant with depth and equal to 0.4 m, and no "drag7' zone has been considered.

The following observations are made from Fig. 3: (i) the maximum shear force in the pile is developed at the level of the slide plane; (ii) for the flow mode, the maximum moment occurs below the slide plane, in the stable soil, and the pile movement is considerably less than the soil movement; (iii) for the short-pile mode, the maximum moment occurs well above the slide plane in the unstable soil, and the soil and pile movements are similar; and (iv) for the intermediate mode, large moments are developed both above and below the slide zone, and the pile head movement can exceed the soil movement.

The largest shear force occurs when the soil slide depth is between about 0.5 and 0.6 times the pile length. The effect of yielding of the pile is to reduce the maximum shear force, especially for slide depths between about 0.25 and 0.9 times the pile length.

Two important practical implications may be drawn from Fig. 3: Firstly, the flow mode creates the least dam- aging effect of soil movement on the pile; if protection of the piles is being attempted, efforts should be made to promote this mode of behaviour. Secondly, the intermediate mode develops the largest shear force and bending moment in the pile; hence, if piles are being used to stabilize the slope, they should be designed so that the intermediate mode of behaviour occurs. This can be done by varying the depth of embedment of the pile in the stable zone in the analysis until a maximum value of shear force is found.

The soil failure mode will depend on the length, diameter, and section of the pile, strength and deformation properties of the pile material, strength properties of the soils in the unstable and stable regions, relative lengths of the pile

li

in the unstable and stable regions, and the spacing between adjacent piles. It is possible to develop design charts that relate the resistance developed by piles to the above vari- ables, as described later in the paper.

Estimation of soil parameters

Key parameters required for lateral response analysis of a pile are Young's modulus of the soil, E,, and limiting lateral pile-soil pressure, p,. Assessment of these parameters is usually made on the basis of ( i) correlation with strength properties of soil; (ii) correlation with in situ test data (e.g., CPT, SPT); ( i i i ) in situ test measurements (e.g., via the pressuremeter of the dilatometer); and (iv) interpretation of lateral pile load test data.

A brief review of some correlations for E, and p, is made below.

Young's modulus, E, For clays, Young's modulus E, is usually related to the undrained shear strength c , as follows:

[51 Es=alcu Assuming a nonlinear analysisris to be used, so that E,

represents a secant modulus for relatively low load levels, the value of a, typically lies between 150 and 400 (Poulos and Davis 1980; Banerjee and. Davies 1978; Decourt 1991).

For overconsolidated clays, Decourt (1991) suggests the following correlation with SPT value N:

For sands, it is customary to assume that the modulus varies linearly with depth, so that

where z is depth below ground surface. Typical values of N, for saturated loose, medium, and dense sands are 1.5, 5.0, and 12.5 MPaIm, respectively (Decourt 1991).

Kishida and Nakai (1977) relate E, to SPT value N as follows:

[8] E, = 1.6 N (MPa)

Ultimate lateral pressure, p, Ito and Matsui (1975) have developed a theory for flow of soil through a row of piles. Their equations show that the limiting pressure p, developed on a pile by flowing soil depends on the strength properties of the soil, overburden pressure, and the spacing between the piles relative to their diameter. Their equations are meant to apply for the portion of the piles in the unstable or moving soil. However, the equations are only valid over a limited range of spacings, since, at large spacings or at very close spacings, the mechanism of flow through the piles postulated by Ito and Matsui is not the critical mode.

In clay soils, it is usual to adopt a total stress approach in which p, is related to undrained shear strength c , as follows:

191 P, = N,C,

where N, is the lateral capacity factor. For a single pile, N , may be assumed to increase linearly from 2 at the

81 2 \ 1

, , Can. keotech. J. Vol. 32, 1995 * h

Fig. 3. Pile behaviour characteristics for various modes.

Deflection (m)

0 O

5 E w

5

10 fl a movement B

15 Deflection

Deflection (m) 0.5 -

5 E

a

Soil

15 Deflection

Moment Shear Pressure

z, /L = 0.2 p, = 0.40m

(a) Flow Mode

Moment (kNn1) . I 000 0 1000

Slide -

Moment

Shear (kN) -500 0 500

Pressure (MPa)

Shear Pressure

z, /L = 0.6 p, = 0.40m

(b) Intermediate Mode .

Deflection (m) Moment (kNm) Shear (kN) 0.5 - 1 000 0 1000 -500 0 500

Deflection Moment Shear

z , /L = 0.9 p, = 0.40m

(c) Short Pile Mode

ressure (MPa)

1 Pressure

Poulos

Fig. 4. Typical geotechnical profiles.

Note: EW =Extremely weathered HW = Highly weathered MW =Moderately weathered SW = Slightly weathered

ground surface to a limiting value of N , = 9 at a depth of 3.5 pile diameters or widths and beyond i.e.,

where z is depth below ground surface; and d is pile diameter or width.

Theoretical studies by Chen and Poulos (1993) provide some indications of the influence of group effects on N,. Such effects may reduce N, if the piles are arranged in a line parallel to the direction of soil movement.

For piles in sands, the simplest approach is to use the suggestion of Broms (1964) in which

11 Py = aK,u:,

where K, is the Rankine passive pressure coefficient, K, = tan2 (45 + $12); $ is the angle of internal friction of soil; u:, is the effective overburden pressure; a is a coefficient ranging between 3 and 5.

Randolph and Houlsby (1984) have developed an analysis for drained conditions in clay in which the coefficient a in eq. 11 is K,.

It is noted by De Beer (1977) and Viggiani (1981) that different values of the coefficients N, and a in eqs. 9 and 11 may apply for the sliding and stable portions of the soil profile. Typically, the values in the stable soil have been taken to be those given in eqs. 10 and 11 above, while the values in the sliding soil have been taken to be about half of those values. However, other than for the near-surface effects, there appears to be no reason why such differences should exist.

\

1 \,

%

Table 1. Soil strength parameters adopted for stability analyses.

Depth below surface c' ' Bulk density

(m) ( k W (") (t/m3)

Fill 10 25 2.0 0-2 5 25 2.0 2-8 5 22 2.0 8-1 1 0 25 2.0 11+ 20 30 2.0

Example of application: State Highway 23, Newcastle, Australia

In 1990, the Roads and Traffic Authority of New South Wales (RTA) commenced construction of a north-south bypass around the city of Newcastle. Part of this project involved construction of an interchange between State Highway 23 (SH23) and a cross road (Sandgate Road). SH23 was to be located in a cutting about 4.5 m below natural surface level, but in parts of the cutting, fill was to be placed for interchange ramps and bridge approach abutments, so that slopes with a total height of up to 8 m were to be created.

As described below, stability analyses were undertaken of various sections along the cutting, and areas were identified in which the factor of safety against instability was considered inadequate. In such areas, stabilizing piles were to be installed, and the design of these piles is detailed in the following sections. A number of alternative options for stabilization were also considered, including use of soldier beams, soil nailing, and construction of retaining walls, but the piling option was chosen because it was assessed to be the lowest cost solution.

Site conditions A summary of the geotechnical profiles revealed by two of the boreholes from the site investigation is given in Fig. 4. No in situ test data on engineering properties were available.

Four soil or rock units were identified at the site: (i) top- soil, typically 0.3 m thick; (ii) high plasticity clay, relatively stiff and probably of residual origin, 1.5-2 m thick; (iii) claystone, fissured and extremely weathered, but with no evidence of slickensides or earlier slips, 5.0-5.5 m thick; and (iv) siltstone; the cored boreholes were terminated in this material.

Groundwater levels immediately after drilling were about 2.6 m below the surface, but appeared to become lower with time and were considered to be subject to sea- sonal fluctuations.

Stability analysis Estimates of the factor of safety against slope instability were made using the following assumptions: ( i) the slip surface was circular and Bishop's simplified method of slices was employed; (ii) the water table was assumed to

,! ' 'Can. ~ e o t e c h . J . Vol. 32, 1995

Fig. 5. Computer safety factor versus chainage.

I s 8

Chainage (m)

Fig. 6. Required stabilizing force (for FS = 1.5) versus chainage.

I Western side

Chainnge (m)

be 1 m below ground level at the toe of the cut, rising to about half slope height level at the head of the slope; and (iii) a surcharge loading of 30 kPa, located 1 m away from the top of the slope, was included to represent the effects of traffic loading.

The shear strength parameters adopted for the analyses are summarized in Table 1 and were based largely on limited laboratory data. It was assumed that the fill material would be similar to the excavated material, but that com- paction would be sufficient for an effective cohesion of 10 kPa to be developed, with an effective angle of friction of 25".

Stability analyses were carried out for slopes along SH23 between chainages 3165 and 3300, at 15 m inter- vals. Slope profiles along both the eastern and western sides were considered.

The analysis results are summarized in Fig. 5, which plots the computed factor of safety as a function of chainage. Because of the potentially severe consequences of slope failure on the operation of this main highway, a factor of safety of 1.5 was selected as the minimum adequate value. Figure 5 indicates that virtually all of the western side, and

*b

Fig. 7. Resistance developed by 1.2 m diameter bored piles, 6 m long.

C/C spacing (m)

41

" 0 1 2 3 4 5

Depth of Plane below Pile Top (m)

Fig. 8. Resistance developed by 1.2 m diameter bored piles, 9 m long. , -

C/C spacing (m)

0 2 4 6 8

Depth of Slide Plane below Pile Top (m)

a considerable portion of the eastern side, had a computed factor of safety less than 1.5 and therefore required some form of stabilization. The minimum safety factor was about 1.15 for chainage 3225 on the western slope, where the cut was about 5 m in natural materials.

Design of stabilizing piles From the detailed output of the stability analyses, the required stabilizing force was computed for each section analyzed, using eq. 3. Stabilizing forces thus computed are plotted against chainage in Fig. 6. The largest forces

Poulos

Fig. 9. Resistance developed by 1.2 m diameter bored piles, 12 m long.

1°00 - 0 2.5 5.0 7.5 10


Fig. 10. Influence of pile length on resistance developed by 1.2 m diameter bored piles at 3.6 m spacing.

" 0 2 4 6 8 10


required were on the western side of the cutting and reached a maximum of about 150 kN/m at chainage 3 180.

Using the program ERCAP, design charts were prepared for bored concrete piles 1.2 m in diameter. The strength properties of soils along the pile were assumed to be those shown in Table 1. Young's modulus of the soil was assumed to increase linearly with depth, from a value of 5 MPa at the surface, at a rate of 3 MPa/m. In the unstable zone, the limiting lateral pressure on each pile was computed in ERCAP from the theoretical solutions of Ito and Matsui (1975), while in the stable zone, the limiting lateral pressure

\ \

I \

81 5 s

Fig. 11. Influence of pile spacing on resistance developed by row of 1.2 m diameter bored piles.

Slide Plane 4 below Pile Top

Pile length (m)

2 3 4 Pile Spacing (m)

Fig. 12. Influence of pile diameter on resistance developed

500

n

E 400

m e, - . - a

300

B a 0 - 0

200 n e, U

5 . m 100 2

0

y row of 1.2 m diameter bored piles.

9 m long piles C/C spacing = 3.0 m

Depth of slide

0.8 1.0 1.2 1.4 1.6 Pile Diameter (m)

on a pile was taken to be 4.5 times the Rankine passive pressure. Each pile was assumed to be reinforced with steel bars, equivalent to an area of 2.5% of the cross- sectional area of the pile. The yield stress of the reinforcement was taken as 260 MPa.

Figures 7 to 9 show the charts for embedded lengths of 6, 9, and 12 m and for centre to centre spacings of 2.4, 3.0, and 3.6 m. In each case, the resistance developed by the pile is plotted against the depth of the sliding plane below the top of the pile. The influence of depth of the

\

81 6 , 'Cart. deotech. J. Vol. 32, 1995 .& a

Fig. 13. Scheme developed for stabilization of slopes with bored piles. Note: 0 represents location of 1.2 m

diameter bored pile

Toe bf slope

Toe of slope \ \

10: E V

0

G 5

b 0 U

C cd * m . d

a 0

Chainage (m)

(A) WESTERN SIDE

Chainage (m)

(B) EASTERN SIDE

sliding plane becomes more marked as the pile length increases, and there appears to be an optimum depth at which pile resistance developed is a maximum; this optimum depth is generally of the order of 0.6 to 0.75 times the length of pile, for which the intermediate mode of soil failure is operative.

Figure 10 summarizes computed pile resistance versus. depth of slide plane, for the three pile lengths considered and for a centre to centre pile spacing of 3.6 m. The pile resistance increases as the depth of slide plane increases, up to the optimum depth. For shallow depths of sliding, pile resistance is independent of pile length, since the domi- nant mechanism is "flow-through" of the soil past the piles. However, for larger slide depths the resistance developed by the pile increases significantly as length of the pile increases.

Figure 11 summarizes the general effect of pile spacing on pile resistance. As would be expected, reducing spacing increases pile resistance significantly.

Figure 12 shows an example of the effect of pile diameter on pile resistance for a given spacing. In general, the resistance developed by a 1.2 m diameter pile is of the order of twice the resistance for a 0.9 m diameter pile. Diameter piles of 1.2 m appear to represent a reasonable compromise between inadequate pile resistance provided by 0.9 m diameter piles and high construction costs that may be associated with 1.5 m diameter piles. Therefore the pile stabilization scheme developed was based on the use of 1.2 m diameter piles.

Pile stabilization scheme Based on the design charts in Figs. 7-12, and the pile resistance requirements for stability in Fig. 6, a pile stabilization scheme was developed. In assessing requirements for stabilizing piles, the following factors were taken into account: (1) The piles must be of a length and spacing that would develop the required resistance (indicated in Fig. 6) to increase the factor of safety for the critical circle to at least 1.5. (2) Other possible failure surfaces were also investigated to check whether a more critical surface existed near or below the pile tips, i.e., to check whether the critical failure surface near or below the pile tips had a safety factor that was still less than 1.5. If that was the case, the pile length was increased accordingly. (3) To be most effective, the lateral location of the piles was such that they were near the lowermost point of the critical failure surface in the soil. This is often found to be in the vicinity of the midpoint of the slope.

A plan of the recommended pile stabilization scheme is shown in Fig. 13. A total of 40 1.2 m diameter piles were used on the western side, with lengths below the surface of the slope varying between 6 and 12 m. In a number of cases, the pile length was increased over the value required to provide the resistance indicated in Fig. 5, SO

that the pile tip was below potential failure surfaces with a factor of safety of less than 1.5. A typical example is shown in Fig. 14 for chainage 3225 on the western side. The original critical circle is shown together with the stabilizing pile as designed and the critical circle for failure

, \ Poulos ' / ' I '

* "i Fig. 14. Typical example of stabilized section: chainage 3225, western side. FS, stabilizing force; HW, highly weathered; SW, slightly weathered.

\ Critical circle vrior to / clay - stabilization \ m(-

~ s s u m e d water table\- -/ HW Siltstone L L i

SW Siltstone

Circle with FS = 1.5 (pile toe extends beyond this)

\

Pile, 1.2 m diameter, 9 m long

0 10 20 Offset (m)

in the vicinity of the toe of the pile. On the eastern side, where stabilizing requirements were more modest, 24 such piles were used. In general, the piles were located within the s l o ~ e . at a distance of between 5 and 6 m from the

A .

toe. The centre to centre spacing varied between 3.2 and 5.0 m.

The recommended scheme involved a total length of piles of 521 m. Construction is planned to commence within the next 2 to 3 years.

Structural requirements for piles Stabil izing piles are subjected to shears and bending moments caused by movement of the soil past the piles. The program ERCAP provided details of the distributions of shear and bending moment along the pile, and a summary of the computed maximum bending moment in the pile is shown in Fig. 15 for a centre to centre spacing of 3.0 m. The maximum bending moment generally increased as the length of pile increased and as the depth to the slide plane increased. For piles longer than about 7 m, and slide plane depths of more than about 4 m, the bending moment could reach the yield moment of the pile section. For these circumstances, it was necessary to increase the amount of reinforcement in the pile.

Conclusions

An approach has been described for the design of piles to stabilize slopes. The resistance that the piles can provide is assessed via an analysis of the response of piles to lateral soil movement. It has been demonstrated that such an analysis identified three possible modes of failure of the soil around the pile: the flow mode, the intermediate mode, and the "short pile" mode. In addition, failure of the pile itself can be associated with any of these modes. The resistance

. *

Fig. 15. ~om~uted.n-hximum bending moment in stabilizing piles. Centre-to-centre spacing = 3.0 m; diameter = 1.2 m.

Estimated yield moment of pile section

Depth of slide plane (m)

-

I

6 9 12 Pile Length (m)

that the pile can provide to help stabilize a slope is great- est when the intermediate mode of soil failure is operative.

The application of the approach to the design of stabilizing piles for a highway embankment has demonstrated that (i) relatively large diameter piles are required to resist shear and moments; ( i i ) the centre-to-centre spacings required typically range between 2 and 4 diameters; and (iii) substantial reinforcement may be required in the pile to avoid the possibility of yielding of the pile itself.

Acknowledgements

The author gratefully acknowledges the permission of the Roads and Traffic Authority of New South Wales (RTA) to publish the information in relation to the State Highway 23 project. M r R . Handley was the Project Manager for the RTA, and his constructive comments are also acknowledged.

References Banerjee, P.K., and Davies, T.G. 1978. The behaviour of axi-

ally and laterally loaded single piles embedded in non- homogeneous soils. GCotechnique, 28(3): 309-326.

Broms, B.B. 1964. Lateral resistance of piles in cohesionless soils. Journal of the Soil Mechanics and Foundations Divi- sion, ASCE, 90(SM3): 123-156.

Chen, L., and Poulos, H.G. 1993. Analysis of pile-soil interaction under lateral loading using infinite and finite elements. Computers and Geotechnics, 15: 189-220.

CPI. 1992. Users manual for program ERCAP. Coffey Part- ners International Pty Ltd., North Ryde, Australia.

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