A practical design approach for piles with negative friction

Proceedings of the Institution of Civil Engineers Geotechnical Engineering 161 February 2008 Issue GE1 Pages 19–27 doi: 10.1680/geng.2008.161.1.19 Paper 14675 Received 01/03/2006 Accepted 29/05/2007 Keywords: foundations/ geotechnical engineering/piles & piling Harry G. Poulos Senior Principal, Coffey Geotechnics Pty Ltd, Lane Cove West, Australia A practical design approach for piles with negative friction H. G. Poulos, BE, DSc(Eng), FIEAust Misconceptions remain in the minds of some pile designers when negative friction effects have to be taken into account. This paper outlines some of these misconceptions, and then describes a relatively straightforward approach for designing piles subjected to negative friction. This approach relies on the consideration of the portion of the pile that is located in the ‘stable’ zone—that is, that part of the ground profile that is not subjected to ground settlements. By designing this portion of the pile to have adequate length and strength, the key design requirements in relation to geotechnical capacity, structural capacity and pile head settlement can be satisfied. The case where the ground settlements extend to a large depth is also described briefly, and it is shown that it may then be prudent to design the piles to settle with the ground, rather than attempt to restrain them from settlement. Some other issues that can affect the response of piles to ground settlements are examined, including the presence of residual stresses in the pile, live load application and group effects. It is demonstrated that preloading a pile has the potential to reduce the axial force induced in the pile by the ground settlements. NOTATION C circumference of pile cu undrained shear strength of clay Es Young’s modulus of soil subject to settlement Esb Young’s modulus of soil in stable zone fb ultimate end-bearing capacity of pile fn negative skin friction fs ultimate skin friction at pile–soil interface FS factor of safety against failure FS2 factor of safety of portion of pile in stable zone PA applied axial force on pile Pmax maximum axial force in pile PNmax maximum downdrag force in pile Pw working load Rug ultimate geotechnical capacity of pile Rug2 ultimate geotechnical capacity of pile in stable zone below depth of soil settlement Rus ultimate structural capacity of pile S
factored loads applied to pile S
max maximum factored axial force in pile S0 settlement of ground surface SR settlement of pile as proportion of ground settlement Geotechnical Engineering 161 Issue GE1 Sw Sall zN ˜Sw ˜Sall äl ög ös settlement at serviceability or working load allowable settlement depth to neutral plane differential settlement at serviceability or working load allowable differential settlement length increment along pile geotechnical reduction factor structural reduction factor 1. INTRODUCTION It has long been recognised that piles located within a settling soil profile will be subjected to negative skin friction. Despite the widespread recognition of the phenomenon of negative skin friction, there remains a misconception that this phenomenon will reduce the ultimate geotechnical axial load capacity of a pile (termed here the geotechnical capacity). As pointed out by Fellenius1 and Poulos,2 among many others, this concept is not valid. Because geotechnical failure of a pile requires that the pile moves (or ‘plunges’) past the soil, negative skin friction cannot be present when this happens, and so the geotechnical capacity will not be reduced by negative skin friction unless there is strain-softening at the pile/soil interface. This is unlikely to occur in soft clays, for which the problem of negative skin friction is most prevalent. The key issues related to negative skin friction are as follows. (a) It will induce additional axial forces in the pile. Fellenius 1,3 has suggested the terminology ‘drag force’ for this induced force, and this terminology will be adopted in this paper. (b) It will cause additional settlement of the pile, which Fellenius1,3 has termed ‘downdrag’. However, to avoid confusion with other connotations of the term ‘downdrag’, the term ‘drag settlement’ will be used herein to refer to this additional settlement induced by negative skin friction. This paper will examine the design requirements for piles subjected to negative skin friction, and will present a relatively simple design approach that can address these requirements. It will then examine some other issues that can influence the magnitudes of drag force and drag settlement: the presence of residual stresses in the pile, the influence of live load, and group effects. A practical design approach for piles with negative friction Downloaded by [] on [25/06/22]. Copyright © ICE Publishing, all rights reserved. Poulos 19 2. KEY DESIGN CRITERIA There are at least three key criteria that must be satisfied in the design of piles subjected to both axial load and negative skin friction. (a) They must have adequate geotechnical capacity to support the imposed loadings. (b) They must have adequate structural strength to withstand the applied axial force and the axial force induced by the ground settlements. (c) The settlements and differential settlements must be within tolerable limits for the structure. 1 where Rug is the ultimate geotechnical capacity of pile (making no allowance for negative friction); FS is the overall factor of safety; and Pw is the working load applied to the pile. Typically, design values of FS range between 2 and 3. (b) In terms of LRFD: 2 3.1. Design for geotechnical capacity Because the presence of negative skin friction does not generally reduce the geotechnical capacity of a pile, the design requirement for geotechnical capacity may be expressed as follows. ög :Rug > S
where ög is the geotechnical reduction factor; Rug is the ultimate geotechnical capacity of the pile (making no allowance for negative friction); and S
is a factored-up combination of loads for the ultimate limit state. Conventional design methods have addressed the first two criteria in terms of an overall factor of safety, whereas some more modern approaches employ load and resistance factored design (LRFD). Both of these approaches will be discussed below. 3. A PRACTICAL DESIGN APPROACH The general problem is illustrated in Fig. 1, where a pile is situated within a soil layer or layers that are settling, and below which there are one or more layers that are not settling. The upper layer will be termed the ‘settling layer’ and the underlying layer(s) will be termed the ‘stable layer’. For simplicity, only a single settling layer and a single stable layer are shown in Fig. 1. The pile is loaded by an axial force PA , and the settlement profile is assumed to decrease linearly with depth from a maximum value S0 at the ground surface to zero at the base of the settling layer. Rug ¼ FS:Pw Typically, ög values range between about 0.4 and 0.9, depending on a number of factors including the level of pile testing (e.g. Australian Standard AS 2159-1995 4 ). 3.2. Design for structural capacity (a) In terms of overall factor of safety: 3 Rus ¼ FSs ð Pmax Þ where Rus is the ultimate structural strength; FSs is the factor of safety for structural strength; and Pmax is the maximum axial force in pile, including the working load and the drag force. (b) In terms of LRFD: 4 ös :Rus > S
max where ös is a structural reduction factor, and S
max is the maximum factored axial force in the pile, including the drag force. (a) In terms of overall factor of safety: PA In computing Pmax or S
max , it is usual to consider various combinations of the applied dead, live, wind and earthquake loads to the maximum drag force PNmax . Typical load factors would be 1.25 to 1.3 for dead load, 1.5 for live load, 1.0 for wind loading and earthquake loading, and 1.2 for the drag force. Most codes will have specific combinations of these loads and forces that have to be considered. S0 Settling zone hs d Lc Stable zone Profile of ground settlement against depth Fig. 1. Basic case of pile subjected to negative friction 20 Geotechnical Engineering 161 Issue GE1 The value of PNmax can be computed as the drag force at the neutral plane, which is the depth (zN ) at which the friction changes from negative to positive, and which is also the depth at which the soil settlement and the pile settlement are equal. Conservatively, this depth can often be taken as the depth of soil movement, that is, at the base of the settling soil layer(s). Alternatively, a more detailed estimation of zN can be made, using (for example) the approach described by Poulos.2 PNmax can be estimated on the assumption that full mobilisation of negative skin friction above the neutral plane has occurred, so that A practical design approach for piles with negative friction Downloaded by [] on [25/06/22]. Copyright © ICE Publishing, all rights reserved. Poulos 5 PNmax ¼ z¼z XN ð f N :C:älÞ z¼0 where fN is the negative skin friction (usually taken to be equal to the positive skin friction); C is the pile circumference; and äl is the length increment along the pile. 3.3. Pile head settlement The design requirements for settlement are as follows: 6 4. AN ALTERNATIVE DESIGN CRITERION FOR CONTROLLING SETTLEMENT To avoid having the pile settle continually as the ground settles, it is proposed that the portion of the pile located below the depth of ground movement should be designed to have an adequate margin of safety against the combined effects of the applied loads and the maximum drag force. It can be shown that, under these circumstances, the depth of the neutral plane then lies below the depth of soil movement. This criterion may be expressed as follows. (a) In terms of factor of safety: Sw < Sall Rug2 > FS2 ð Pw þ PNmax Þ 9a 7 ˜Sw < ˜Sall where Sw is the settlement at the working or serviceability load; Sall is the allowable or tolerable settlement for the supported structure; ˜Sw is the differential settlement at the working or serviceability load; and ˜Sall is the allowable or tolerable differential settlement for the structure. Values of Sall and ˜Sall depend on the type of structure and on the general ground conditions. Typical values are suggested by Bowles 5 and Tomlinson. 6 There are at least two means of estimating the values of Sw and ˜Sw : (a) via a soil–pile interaction analysis, for example via finite element analysis7,8 or boundary element analyses 7,9,10 (b) via an approximate analysis such as that set out by Poulos.2 It has been demonstrated by Poulos 2 that, if the neutral plane lies at or below the depth of ground settlement, the pile settlement will reach a limiting value and will then not continue to settle as the ground continues to settle. In this case, the settlement Sw of the pile head at the working or serviceability load can be estimated as follows. 8 Sw ¼ S1 þ S2 þ S3 where Rug2 is the ultimate geotechnical capacity of the pile in the stable zone below the depth of soil settlement; and FS2 is the factor of safety for the portion of the pile in the stable zone. (b) In terms of LRFD: ög2 :Rug2 > S
max 9b where ög2 is the geotechnical reduction factor for the stable zone, and S2max is as defined above in equation (4). The above approach will be evaluated below, where the issue of selection of a suitable value of FS2 or ög2 will also be considered. 4.1. Evaluation of proposed alternative design criterion In order to evaluate the proposed alternative design criterion, two hypothetical but typical problems have been analysed, as shown in Fig. 2. The first involves a single pile located in a 20 m thick soft clay layer that will experience a ground surface settlement of 100 mm, underlain by a stiff clay layer. This will be denoted as an ‘end-bearing’ pile. The second case involves an identical settling layer as for the end-bearing pile, but the underlying layer is a medium clay layer with considerably smaller strength and stiffness than in the first case. This will be PA where S1 is the elastic compression of the portion of the pile shaft in the settling zone, due to the applied load on the pile head, Pw ; S2 is the elastic compression of the portion of the pile shaft in the settling zone, due to the induced drag forces; and S3 is the settlement of the portion of the pile in the stable zone. S1 and S2 can be computed from simple column compression theory, taking account of the fact that, for S2 , the axial drag forces increase with depth in the settling zone. S3 can be computed adequately from elastic theory for the length of the pile embedded in the stable zone and subjected to an applied load equal to the applied pile head load ( Pw ) plus the maximum drag force in the pile, PNmax . In many cases, designing the pile so that it does not continue to settle with increasing ground settlement is a desirable condition, and leads to an alternative design criterion that is described in more detail below. Geotechnical Engineering 161 Issue GE1 PA S0 Settling soft clay Settling soft clay cu ⫽ 22 kPa fs ⫽ 22 kPa Es ⫽ 2 MPa ‘Stable’ stiff clay cu ⫽ 500 kPa fs ⫽ 200 kPa fb ⫽ 4·5 MPa Esb ⫽ 100 MPa 20 20 d ⫽ 0·5 d ⫽ 0·5 Lc ‘Stable’ stiff clay cu ⫽ 80 kPa fs ⫽ 60 kPa fb ⫽ 0·72 MPa Esb ⫽ 30 MPa (a) (b) Fig. 2. Cases analysed for design study: (a) end-bearing pile; (b) floating pile A practical design approach for piles with negative friction Downloaded by [] on [25/06/22]. Copyright © ICE Publishing, all rights reserved. Lc Poulos 21 denoted as the ‘floating pile’ case. For simplicity, the results will be described in terms of the conventional factor of safety concept. Figure 3 shows the computed overall factor of safety FS as a function of the length of pile in the stable zone, Lc . FS is defined here as the ratio of the sum of the pile resistances in the settling zone and the stable zone, divided by the applied load. It is recognised that some foundation designers are hesitant to include the first component of pile resistance, as it initially acts as a downdrag force, and becomes a resistance only when the pile moves sufficiently to settle more than the surrounding soil. Nevertheless, it is, in principle, an available component of resistance at the ultimate limit state. As would be expected, FS increases with increasing Lc and decreasing applied load PA . The corresponding relationships for the floating pile are shown in Fig. 4. From these figures, the required value of Lc for a specified factor of safety can be obtained, and these values are shown in Table 1 for a design FS of 2.5. Clearly, a larger value of Lc is required as PA increases. Figs 3 and 4 may be used to assess the necessary length of pile in the stable zone to satisfy the overall geotechnical capacity criterion. For example, for the endbearing pile with a working load of 1.5 MN applied at the pile head, Fig. 3 reveals that, for a factor of safety of 2.25, the necessary value of Lc is about 6 m. Figures 5 and 6 show the computed factor of safety FS2 in the stable zone, again as a function of Lc and PA . The maximum drag force PNmax has been computed to be at the base of the settling layer, and has a magnitude of 0.691 MN. As with the overall factor of safety, FS2 increases with increasing Lc or decreasing PA . The computer program PIES, developed at the University of 7 Overall factor of safety Factor of safety in stable zone PA ⫽ 1·0 MN 6 PA ⫽ 1·5 MN 5 PA ⫽ 2·0 MN 4 3 2 1 0 0 4 6 8 10 12 Length of pile in stable zone, Lc: m 2 14 9 PA ⫽ 0·8 MN 6 PA ⫽ 1·2 MN Factor of safety in stable zone Overall factor of safety 7 5 4 3 2 1 0 0 5 10 15 20 Length of pile in stable zone, Lc: m 25 Fig. 4. Overall factor of safety against pile length in stable zone: floating pile Case Length in stable zone, Lc :* m 2·5 2·0 1·5 1·0 PA ⫽ 1·0 MN PA ⫽ 1·5 MN PA ⫽ 2·0 MN 0·5 0 4 6 8 10 12 Length of pile in stable zone, Lc: m 2 14 16 Fig. 5. Factor of safety in stable zone against pile length in stable zone: end-bearing pile PA ⫽ 0·4 MN 8 3·0 0 16 Fig. 3. Overall factor of safety against pile length in stable zone: end-bearing pile 3·5 Total pile length: m 2·5 PA ⫽ 0·4 MN PA ⫽ 0·8 MN PA ⫽ 1·2 MN 2·0 1·5 1·0 0·5 0 0 5 10 15 20 Length of pile in stable zone, Lc: m 25 Fig. 6. Factor of safety in stable zone against pile length in stable zone: floating pile Applied load, PA : MN Pile head settlement: mm PIES program Simple method End bearing Floating 6 18 26 38 1.5 0.8 12.5 9.9 12.0 10.4 * For overall factor of safety of 2.25. Table 1. Comparison of computed settlements 22 Geotechnical Engineering 161 Issue GE1 A practical design approach for piles with negative friction Downloaded by [] on [25/06/22]. Copyright © ICE Publishing, all rights reserved. Poulos For each of the cases shown in Fig. 2, PIES has been used to compute the influence of the factor of safety of the portion of the pile in the stable zone (and hence the length of pile Lc in the stable zone) on the drag settlement of the pile induced by the ground settlements, and on the maximum load in the pile. The analysis results are shown in Figs 7 and 8, and reveal that if FS2 ¼ 1.0, the pile continues to settle as the soil settlement increases, but for FS2 ¼ 1.25 or greater the pile settlement appears to reach a limiting value, regardless of the soil settlement, while the drag force induced in the pile is also reduced. Figure 9 shows Fig. 8 re-plotted in dimensionless form in terms of the ratio of the drag settlement SD to the ground surface settlement S0 , against FS2 for both the floating and end bearing cases, and it can be seen that SD /S0 decreases with increasing FS2 : that is, the relative drag settlement reduces as the factor of safety in the stable zone, FS2 , increases. A single regression line can be drawn through the points, and, as 60 Pile head settlement: mm FS2 ⫽ 1·0 50 FS2 ⫽ 1·25 40 FS2 ⫽ 1·5 FS2 ⫽ 2·0 30 20 10 0 0 50 100 150 200 250 300 350 400 Ground surface settlement: mm 450 500 Fig. 7. Evolution of pile settlement: End-bearing pile Pile head settlement: mm 14 12 10 8 6 FS2 ⫽ 1·0 FS2 ⫽ 1·25 4 FS2 ⫽ 1·5 2 FS2 ⫽ 2·0 0 0 50 100 150 200 250 300 350 400 450 Ground surface settlement: mm Fig. 8. Evolution of pile settlement: floating pile Geotechnical Engineering 161 Issue GE1 500 Pile settlement/ground settlement, SR Sydney, has been used to analyse both these problems. PIES uses a simplified boundary element approach to analyse the settlement and load distribution within a single pile or a symmetrical pile group, subjected to axial loading and to externally imposed ground settlements. Mindlin’s equations for an elastic continuum are used as the basis for computing the soil movements due to pile loading, but non-linearity is allowed for by incorporating a hyperbolic relationship between soil/pile interface stiffness and applied stress level, and by specifying limiting skin friction and end bearing values. 1·0 0·9 0·8 0·7 0·6 0·5 0·4 0·3 0·2 0·1 0 End bearing pile Floating pile Regression line SR ⫽ 0·097(FSs)^(⫺1·36) 0 0·5 1·0 1·5 2·0 2·5 3·0 3·5 4·0 Factor of safety in stable zone, FSs 4·5 Fig. 9. Dimensionless drag settlement against factor of safety in stable zone indicated in Fig. 8, beyond about FS2 ¼ 1.25 there is little further reduction in the relative drag settlement. For the end-bearing pile, subjected to an applied load of 1.5 MN, referring to Fig. 5, a value of FS2 of 1.25 requires a value of Lc of about 6 m, which (by coincidence) is the same as the value required for the overall factor of safety criterion with FS ¼ 2.25. This implies that the overall capacity criterion and the settlement control criterion govern this design equally. For the floating pile, subjected to a load of 0.8 MN, Fig. 6 shows that a value of FS2 of 1.25 requires a length in the stable zone, Lc , of about 18 m. From Fig. 4, this value of Lc corresponds to an overall factor of safety of about 3.1. Thus, in this case, it is the settlement control criterion that governs design, since an overall factor of safety of 2.25 would require a value of Lc of only about 11 m. Table 1 compares the total pile head settlements (due to both applied load and negative friction) computed from the PIES program with the simple approach set out above in equation (8), involving the summation of the three components S1 , S2 and S3 . In this case S3 has been computed from the Randolph and Wroth 11 equations. It can be seen from Table 1 that the settlements from the simple approach agree well with those from the PIES program. The latter program also confirms that the settlement reaches a limiting value and does not continue to increase with increasing ground settlements beyond a ground surface settlement of about 150 mm. The pile head settlements shown in Table 1 would normally be expected to be tolerable for most structures, even when group effects are allowed for. From the limited study described herein it would appear that, from a practical design viewpoint, the use of a factor of safety in the stable zone, FS2 , of 1.25 should be adequate to avoid having the piles settle continuously as the ground settlement increases. More generally, this ‘target’ factor of safety in the stable zone may vary, depending on the ratio of the shaft and base resistances in the stable zone. From a design viewpoint, if one or other component provides the predominant proportion of the resistance, a somewhat larger factor of safety may be desirable to compensate for the reduced ‘redundancy’ that is present when both components contribute almost equally to the resistance in the stable zone. Because of the number of different load cases that need to be A practical design approach for piles with negative friction Downloaded by [] on [25/06/22]. Copyright © ICE Publishing, all rights reserved. Poulos 23 considered in LRFD design, it is less easy to develop a design criterion for the geotechnical factor ög2 for the stable zone. However, if an average load factor of 1.25 is assumed, then a value of FS2 of 1.25 translates to a value of ög2 of 1.0 (note that a larger and more realistic average load factor would lead to an even larger implied value of ög2 ). In other words, in LRFD design, the design criterion (equation 9(b)) requires that the unfactored capacity of the portion of the pile in the stable zone should equal or exceed the factored load combinations, including the drag load. PA S0 Soft clay cu ⫽ 22 kPa 20 fs ⫽ 22 kPa Es ⫽ 2 MPa Soil movement profile fb ⫽ 8 MPa Esb ⫽ 500 MPa Fig. 10. End-bearing pile analysed for residual stress effects 2·5 2·0 1·5 1·0 With residual stresses and soil movements With residual stresses and no soil movements No residual stresses, no soil movements No residual stresses, with soil movements 0·5 0 0 10 20 30 40 Pile settlement: mm 50 60 70 (a) The pile has been loaded to failure and then unloaded, simulating installation by driving or jacking. 13 This stage induces a residual stress distribution in the pile. (b) A working load of 0.9 MN has been applied to the pile. (c) A ground settlement profile has been applied to the pile, with the maximum ground surface settlement being 500 mm and decreasing with depth to zero at a depth of 20 m. (d ) The pile has then been loaded to failure. An analysis has also been carried out where the first step is omitted, thus representing a pile with zero initial residual stress. Figure 11 shows the load–settlement curves for the endbearing pile with and without residual stresses. It can be seen that the pile with residual stresses undergoes greatly reduced settlement compared with the initially stress-free pile. Fig. 12 shows the evolution of pile head settlement with increasing ground surface settlement, and again highlights the difference in behaviour between the piles with and without residual stress. This figure also shows that the pile with residual stress reaches a limiting or equilibrium settlement when the ground surface settlement is about 60 mm. In contrast, the initially stress-free pile continues to undergo increasing settlement with increasing 35 Pile head settlement: mm 6.1. Effects of residual stresses Analyses of piles subjected to negative skin friction almost invariably assume that the pile is initially stress-free, but this is generally not a realistic assumption, especially for driven or jacked-in-place piles. To examine the possible effects of residual stresses on pile drag loads and drag settlements, the case shown in Fig. 10 has been analysed using the program PIES. This case represents a primarily end-bearing pile, and the following simulation stages have been applied. Geotechnical Engineering 161 Issue GE1 Weak rock Fig. 11. Load–settlement curves for end-bearing pile, with and without residual stresses 6. OTHER FACTORS 24 d ⫽ 0·5 Pile load: MN 5. CASES WHERE SOIL SETTLEMENTS OCCUR TO CONSIDERABLE DEPTH In most foundation designs emphasis is placed on minimising settlements, and this often means supporting the structure on end-bearing piles that are founded on rock or on a stiff stratum. However, there may be cases in which such a strategy is not feasible or is impractical—for example, where there is a deep layer of soft clay, most of which is subjected to ground settlements. Such situations are common in certain urban areas (e.g. Bangkok, Mexico City, Houston) because of the pumping of groundwater for water supply. In such cases it is almost futile to attempt to stop the pile settling as the ground continues to settle. Instead, it seems preferable to accept that continuing settlement of the foundation is inevitable, and then to attempt to have the foundation settle the same amount as the ground. In this way, excessive differential settlements between the structure and the surrounding ground are avoided. In such cases, a proper pile–soil interaction analysis should be carried out to identify the length of piles for which the difference between the pile head settlement and the ground surface settlement is an acceptable value. Poulos 12 describes the application of this design philosophy to piled raft foundations. 30 25 20 With residual stresses No residual stresses 15 10 5 0 0 50 100 150 200 250 300 350 Soil surface settlement: mm 450 500 Fig. 12. Development of pile settlement with soil settlement; applied load ¼ 0.9 MN A practical design approach for piles with negative friction Downloaded by [] on [25/06/22]. Copyright © ICE Publishing, all rights reserved. 400 Poulos ground surface settlement, even at a ground surface settlement of 500 mm, although there is no further change in the downdrag load or the stress acting on the pile toe. Figure 13 shows the computed relationship between maximum load in the pile and the ground surface settlement. The initially stress-free pile experiences a slightly reduced maximum load compared with the pile with initial residual stresses, but the difference is relatively minor. The computed pile base pressures at various stages are shown in Fig. 14. It is clear that the pile with residual stress has a ‘preloaded’ base and is therefore subjected to less base stress change during its history. As a consequence, the tip penetration is less, and this is reflected in a smaller pile head settlement. Similar analyses have been carried out for a predominantly floating pile, and trends similar to those for the end-bearing pile are noted, However, because the initial residual stresses in a floating pile are less (because of the smaller end bearing stiffness and capacity), the relative reduction in settlement of the pile with residual stresses is less than for the end-bearing pile. Nevertheless, it would appear that some benefits may be gained if a pile has initial residual stresses prior to the application of load and ground movement. This in turn suggests the following. (a) Piles that are driven or jacked into the ground (and which therefore have initial residual stresses) are likely to settle less under the action of negative skin friction than bored piles, where the initial residual stresses may be less. (b) Preloading of bored piles prior to putting them into service may reduce the potential for future settlements under the action of applied loads and ground movements. 6.2. Effects of live load There is a perception among some engineers that the application of live load can remove the effects of negative skin friction and reduce drag forces. To examine the validity of this concept, the example of the end-bearing pile shown in Fig. 2 has been examined using the program PIES. The pile, of total length 25 m (and thus with a 5 m embedment into the stable zone), has been subjected to the following history. (a) Dead load of 1.0 MN applied (representing an overall factor of safety of about 3). (b) Application of ground settlement linearly decreasing from 100 mm at the ground surface to zero at 20 m depth. (c) Application of additional (live) loads of increasing magnitude. Figure 15 shows the computed relationship between maximum pile load and the additional live load, and Fig. 16 shows the 3·5 Maximum load in pile: MN 1·6 1·4 1·2 1·0 0·8 0·6 With residual stresses No residual stresses 0·4 0·2 0 0 50 100 150 200 250 300 350 Soil surface settlement: mm 400 450 Maximum load in pile/dead load 1·8 3·0 2·5 2·0 1·5 1·0 With 100 mm ground settlement 0·5 500 No ground settlement 0 0·5 0 Fig. 13. Development of maximum pile load with soil settlement. Applied load ¼ 0.9 MN 1·0 Live load/dead load 1·5 2·0 Fig. 15. Effect of live load on maximum pile load 8 No residual stresses 90 7 With residual stresses 80 Pile head settlement: mm Base stress: MPa 9 6 5 4 3 2 1 0 Initial 900 kN 500 mm soil movement Failure No ground settlement 70 60 50 40 30 20 10 0 Stage 0 Fig. 14. Effect of residual stresses on pile base stress at various stages Geotechnical Engineering 161 Issue GE1 With 100 mm ground settlement 0·5 1·0 1·5 Live load/dead load 2·0 2·5 Fig. 16. Effect of live load on pile head settlement A practical design approach for piles with negative friction Downloaded by [] on [25/06/22]. Copyright © ICE Publishing, all rights reserved. Poulos 25 6.3. Group effects It is becoming recognised that group effects may be beneficial in relation to the effects of negative skin friction. To examine the general nature of group effects, the program PIES has been used to analyse a group of nine piles, as shown in Fig. 17, with the ground profile being that of the end bearing case shown in Fig. 2. Each pile is assumed to have a length of 25 m and to be subjected to a load of 1.5 MN, thus giving an overall factor of safety of about 2 against geotechnical failure. A ground surface settlement of 200 mm is then imposed on the piles, decreasing from a maximum at the surface to zero at 20 m depth. The induced pile loads and settlement are examined for the corner and centre piles of the group, and also for a single isolated pile. Figure 18 shows the computed pile head settlement as a function of the ground surface settlement. It can be seen that (a) the pile head settlements increase (but at a diminishing rate) with increasing soil surface settlement; (b) the centre pile settles more than the corner pile (c) both piles in the group settle considerably more than a single isolated pile. 1·25 1·25 1·25 30 Applied load ⫽ 1·5 MN Pile head settlement: mm corresponding relationship for pile head settlement. These figures show that the maximum load in the pile and the pile head settlement continue to increase with increasing live load. When the applied live load is approximately equal to the dead load, the maximum load equals the applied load: that is, the drag force due to the ground settlement is reduced such that the maximum load is now at the pile head. The pile head settlement also becomes similar to the settlement that would have occurred if the ground settlement had not been imposed. From a practical viewpoint, it would appear that, at least in the example considered, the amount of live load that would need to be added to relieve the negative friction effects is far greater than would normally be allowed. Thus it may be concluded that negative friction effects are unlikely to be completely removed when normal magnitudes of live load are applied. S0 Settling zone (soft clay) 10 Corner pile – group Centre pile – group 5 PA ⫽ 1·5 MN/pile Stable zone (stiff clay) Ground settlement profile Geotechnical Engineering 161 Issue GE1 60 80 100 120 140 160 Ground surface settlement: mm 180 200 Figure 19 shows the computed relationship between the maximum load in each pile and the ground surface settlement. The maximum load increases with increasing ground settlement, and is less for the centre pile than for the corner pile. The rate of increase for both the group piles is, however, significantly lower than for a single isolated pile. It is not until relatively large ground settlements occur that the loads in the group and single piles become similar. This characteristic is consistent with that found by Kuwabara and Poulos. 14 It can therefore be concluded that group effects may be beneficial in terms of the induced loads in the piles, especially for relatively small magnitudes of ground movement. However, at normal working loads the pile head settlement is still increased because of group effects. 7. CONCLUSIONS This paper has demonstrated that designing piles to account for negative skin friction requires three criteria to be satisfied: overall geotechnical capacity, structural capacity of the pile itself, and settlement control. For this last criterion, it has been shown that settlements can be limited by having the length of pile in the stable (non-settling) zone such that there is a factor of safety of about 1.25 in that zone against the combined effects of applied load and drag load due to negative skin friction. If this condition is satisfied, then the settlement Applied load ⫽ 1·5 MN 2·0 1·5 Corner pile – group 1·0 Centre pile – group 0·5 Single pile 0 50 100 150 Ground surface settlement: mm 200 Fig. 19. Maximum load against ground settlement for various piles in group Fig. 17. Pile group example 26 40 Fig. 18. Pile settlement against ground surface settlement for various piles in group 0 5 20 0 2·5 PA 20 15 Single pile Maximum pile load: MN PA 20 0 1·25 PA 25 A practical design approach for piles with negative friction Downloaded by [] on [25/06/22]. Copyright © ICE Publishing, all rights reserved. Poulos reaches a limiting value and does not continue to increase if the ground continues to settle. A simple approach can then give an adequate estimation of the pile head settlement. The influence of other factors on induced drag loads and drag settlements is also examined. It is found that the presence of residual stresses in a pile tends to reduce the drag settlement considerably, especially if the pile has a relatively large end bearing capacity and stiffness. This suggests that preloading a pile may have a beneficial effect in reducing drag settlements. The application of live load to a pile does not reduce the total load in the pile, but rather reduces the relative contribution that the drag load makes to the overall maximum pile load. Group effects are generally beneficial and lead to a significantly lower rate of development of drag force and drag settlement with increasing soil settlement than is the case for an isolated pile. ACKNOWLEDGEMENTS The author gratefully acknowledges the valuable comments of Patrick K. Wong of Coffey Geotechnics. REFERENCES 1. FELLENIUS B. H. Recent advances in the design of piles for axial loads, dragloads, downdrag, and settlement. In Urban Geotechnology and Rehabilitation, Seminar sponsored by ASCE Metropolitan Group, New York, April 22–23, 1998. 2. POULOS H. G. Piles subjected to negative friction: a procedure for design. Geotechnical Engineering, 1997, 28, No. 1, 23–44. 3. FELLENIUS B. H. Results from long-term measurements in piles of drag loads and downdrag. Canadian Geotechnical Journal, 2006, 43, No. 4, 409–430. 4. STANDARDS AUSTRALIA. Piling—Design and Installation. Standards Australia, Homebush, Australia, 1995, AS 2159. 5. BOWLES J. Foundation Analysis and Design, 4th edn. McGraw-Hill, New York, 1988. 6. TOMLINSON M. J. Foundation Design and Construction, 7th edn. Pearson Education, Harlow, 2001. 7. LEE C. Y. Pile groups under negative friction. Journal of Geotechnical Engineering, ASCE, 1993, 119, No. 10, 1587– 1600. 8. COMODROMOS E. M. and BAREKA S. V. 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Downdrag forces in group of piles. Journal of Geotechnical Engineering, ASCE, 1989, 115, No. 6, 806–818. What do you think? To comment on this paper, please email up to 500 words to the editor at journals@ice.org.uk Proceedings journals rely entirely on contributions sent in by civil engineers and related professionals, academics and students. Papers should be 2000–5000 words long, with adequate illustrations and references. Please visit www.thomastelford.com/journals for author guidelines and further details. Geotechnical Engineering 161 Issue GE1 A practical design approach for piles with negative friction Downloaded by [] on [25/06/22]. Copyright © ICE Publishing, all rights reserved. Poulos 27