Further discussion on 'An assessment of design methods for piled embankments,' by D Russell and ND Pierpoint, Ground Engineering November 1997. Discussion by Dr Dave Tonks and Dr Rob Hillier, EDGE Consultants UK
The paper and ensuing discussion (BC Slocombe and AL Bell, GE March 1988) make a valuable contribution to developing practical and appropriate design methods for this complex new technique. We also refer to related discussion in this topic at the recent University of Sheffield/EPSRC seminar on Consolidation of Soft Ground, 15 January, reported by Dr Hird in the March issue of Ground Engineering.
The authors have considered four possible design approaches. Our experience of examining this type of scheme for several recent/ongoing projects suggests that the more conservative approaches offer little or no savings over say a conventional piled reinforced concrete slab. We believe the method has potential for significantly more economic solutions in some situations, but have reservations about some of the design methods and the detail of their implementation. We are pleased to note the work reported is part of ongoing study and offer some comments accordingly.
The general design problem relates to any stabilised layer to be constructed over piles or stone columns. This implies that the underlying soil is weak and without columns/piles would undergo unacceptable settlement under the applied loading. However, the extent and implications need careful definition, as do the stress distributions resulting from the piles/stone columns. Acceptable total and differential settlements of the final upper surface need to be specified. In some circumstances these settlements may increase with time. Thickness of the fill is of considerable importance.
For a reinforced concrete raft on piles the stress distributions, and hence the design methods, are well established, if ground support is ignored. It has long been known that economies are possible by including for soil support (soil-structure interaction), although this is not regularly utilised. Over stone columns, the composite column/soil support may be utilised. However, there are still considerable design uncertainties (partly related to the construction methods, power of plant and quality control). Engineering judgment and experience play a substantial role.
Use of a reinforced soil raft is rather similar, but with suitably specified soils in place of concrete and geosynthetic as opposed to steel reinforcement. In the absence of reinforcement, current practice for stone columns would suggest a stone raft. (The writers have also successfully used lime and lime/cement stabilised soil rafts over stone columns and have adopted the expedient of specifying strengths and stiffnesses for these equal to or better than equivalent stone fill. Slocombe and Bell refer to p' 45 at the Second Severn Crossing (SSC).
The authors used 40 here. By contrast, the A13 used a relatively weak fill, with '=30 and E = 20MPa. Can the authors comment further on the influence of fill strength and stiffness? (Incidentally, noting the strains, are critical state parameters appropriate?)
The Terzaghi and Hewlett & Randolph methods do allow for '. Does this account for the differences in their predictions for the two cases (relatively high loads at A13, relatively low at SSC)? The results are so similar one might wonder if they could amount to alternative formulations of the same principles for these particular circumstances. However, the Terzaghi method simply refers to K, enigmatically described as the ratio of horizontal to vertical stress. Could it be that the forces involved can vary, either between active and passive conditions, or possibly some lesser range, depending what is done and/or what is required? If so, the question still arises whether the present formulation fits the problem or whether other factors apply.
Each method relates to height of fill. This can be related back to the Stress Reduction Ratio for each. At lesser fill heights there will be less overall loading. However as the ratio of pile spacing to fill height increases, so will the relative surface deflection. The writers are not aware of a design basis which systematically relates surface performance (settlements/gradients) to the fill thickness. It appears logical that the fill should be better quality (stronger/stiffer) and/or its thickness should be greater for more demanding surface performance requirements.
An angular distortion of 1 in 1,000 was adopted at SSC. This converts to less than 2mm differential settlement over column centre to midpoint (2.5m centres, square grid). This is clearly very demanding, especially in the long term, and may depend considerably on the 4.3m embankment height (ie around 1.7 x the column spacing)
An angular distortion exceeding 1 in 1,000 might be significant in some applications, especially where it gave a regular 'waviness' as a systematic reflection of the underlying column pattern. This would be an increasing risk for thinner embankments.
We have some concerns about the distribution of tensile forces within the geosynthetic(s). The key points would seem to be the in-plane stress concentrations, especially over and at the edges of the pile cap. Suitable detailing appears important here to avoid abrasion damage and ensure suitable load transfer. Did the authors' analyses shed any light on this aspect?
Assuming transfer of all loads to the columns, most of the design methods lead to high reinforcement requirements. Conversely, the trials and experience give some confidence in an economic and appropriate method at least under some circumstances. In seeking to reconcile these two aspects, we see four main explanations:
1. Allowing for the underlying ground. Russell and Pierpoint's March response elegantly demonstrates that allowing for strength and stiffness of the underlying ground greatly reduces loadings. Nonetheless, we have reservations about invoking this soil support in design.
This is not conventionally done. We agree this occurs in the short term, but the long term situation becomes very complex. Indeed satisfactory short term performance is no guarantee of long term suitability. To include the benefit of the underlying ground, it will be necessary to model the soil consolidation and address the long term settlements. In practice, stone columns at close centres are likely to give consolidation settlement more than 90% complete after a year in all but the most impermeable soil. This would not be the case for piles.
2. Short term/long term performance of the geosynthetics. We assume the long term properties were applicable. The short term performance of the geosynthetics may be considerably better. However, the higher tensile forces (and corresponding stiffnesses and strains) given by some of the design methods would be beyond all but the strongest geosynthetics. Can the authors shed any more light on the relative influence of the geosynthetic properties?
3. Soil/reinforcement interaction. The authors discuss 'The Guido Design Method' (Ref 4). This work has been invoked on various occasions to justify apparent beneficial effects of geogrids. The writers agree such effects can occur and may relate to some extent to interlocking behaviour. However, Guido's work involved laboratory tests for footings founded on granular material in a confined large box with rigid base and walls, which applied significant constraints. We would caution against application of these particular results outside the said closely defined limits. We do not believe Guido's work is strictly relevant to this problem or constitutes a design method.
Further laboratory work and possibly field testing may clarify these effects, particularly the relative benefits of different types of reinforcement and use of several layers (noting that strains in the different layers are likely to be very different).
4. Construction deformations. The method of construction can effectively 'prestress' the system. Thus the basal reinforcement becomes increasingly stressed whilst each newly constructed layer is compacted to a flat upper surface, partly taking out the settlements during construction. The key questions then are:
(a) what are the practical limits of what is/can be done?
(b) what are the conditions under which the reinforcement could fail (minimum layer thickness, maximum compactive effort, minimum underlying strength, etc.)?
(c) what are the minimum requirements to achieve stated tolerances at surface?
(d) what are the short term/long term relationships?
We suggest the answers to these questions affect the earth pressure coefficients. For example, good compaction of a strong stone might lock in substantial horizontal forces, having a beneficial effect on arching. This might be incorporated in the Terzaghi K value (see above).
Russell and Pierpoint's numerical modelling techniques may well provide a useful means of further assessing these effects. We agree that the 'yardstick must be validated by field experience'. However, to enable confidence in application to each varying situation, without the need for trials in due course, more cogent design methods are required, fitting and building on such experience.
It is hoped this contribution may assist in assessing the most appropriate 'benefits' and hence help towards appropriate and economic applications of this technique.
Authors' response D Russell and ND Pierpoint, Mott MacDonald, Croydon
The authors are grateful for the discussers' comments on the ongoing research into the behaviour of piled embankments. Some of the discussers' points have already been investigated and for these, results are presented that may be of some interest. For the remainder, the authors provide their opinion and plans for further research. Responses to the points raised have been collated under five headings; embankment fill material, reinforcement, support system, subsoil and piled embankments.
Embankment fill material
The properties of the fill material are clearly a major factor in the behaviour of the piled embankment system. The factors that affect the fill performance are the strength (cohesion, friction and dilation), the stiffness and the initial conditions.
Previously the authors have carried out parametric studies in 2D looking at the influence of each of these parameters. These studies imply that there is little benefit achieved for fill friction angles above 30. However, in Kempton et al (1998) it is clearly demonstrated that 3D analyses are necessary to model the piled embankment behaviour. The authors are currently carrying out a series of parametric studies for the 3D case and will present the results in a future publication.
The authors agree with the discussers and the British Standard (BS8006) assertion that large strains are prevalent and that a critical state angle of friction should be used for such analyses. This is particularly the case in the area of fill adjacent to the pile cap where large shear strains can develop.
In the analysis of the Second Severn Crossing, an angle of friction of 40 was used for the embankment fill. The authors believe that this is a reasonable upper bound to the critical state value for this rockfill material and feel that a peak angle of friction is inappropriate. However based on preliminary results from the 3D parametric study, the authors believe that the use of a peak value p' = 45 (as suggested by Slocombe and Bell) in the analysis would not have significantly changed the results.
The discussers mention the use of lime and lime/cement stabilised fill used to form a raft over piles. The authors would be interested to know details of these schemes and the performance of the system. Parametric studies have shown that reliable cohesion in the fill significantly reduces the Stress Reduction Ratio.
The discussers have identified the importance of the earth pressure coefficient. This is a complex issue and several factors need to be considered:
Initial K Value. During construction, high horizontal stresses may be generated within each layer of fill as it is placed due to the effects of compaction. If it is assumed that the passive limit is reached as a result of this compaction, an initial earth pressure coefficient can be evaluated. However, during subsequent increases in embankment height, the vertical stress increases more rapidly than the horizontal stress and the earth pressure coefficient reduces. For higher embankments the earth pressure coefficient will approach the coefficient of one dimensional compression (K0) at the base of the fill and the influence of compaction in the earth pressure coefficient will be lost.
Prestressing. As the discussers suggest, there will be some degree of prestressing as the embankment is constructed and the fill deforms laterally. This force is assumed to be transferred to the reinforcement as for a conventional basally reinforced embankment. Part of the continuing research study is to investigate the interaction between the components of reinforcement tension generated by the lateral spreading and the arching effects, and confirm whether the lateral and arching components of the reinforcement tension are additive as suggested in BS8006. It should be noted that the lateral component of force is not taken into account in the analyses presented to date.
Consolidation. As the subsoil begins to consolidate arching develops and the fill above the pile cap tends towards an active condition and the material above the reinforcement tends towards a passive condition. This implies a consistent K value above the pile edge for a given ' value. Figure 1 shows the K values for a typical 3D analysis with ' = 40. Figure 2 shows the predicted variation of the Stress Reduction Ratio from 3D FLAC for various initial K values. As can be seen the 3D FLAC analyses predict negligible differences in the Stress Reduction Ratio for various initial K values. This supports the assumption of a constant K value as the arching mechanism develops.
The discussers have asked whether the difference in behaviour between the Second Severn Crossing and the A13 is due to the difference in fill strength ('=40 and 30 respectively). Although this may have contributed to the difference the authors believe that the major effect is due to the difference in stiffness of the reinforcement. Stiffer reinforcement attracts more load and limits movement. The low stiffness reinforcement in the Second Severn Crossing analysis resulted in vertical deflection of the reinforcement of almost 500mm with a correspondingly low reinforcement tension.
The discussers point out that the distribution of tension is likely to be non-linear along the length of the reinforcement. In the analyses presented by the authors to date it has been assumed that the bond between the reinforcement and the pile is perfectly smooth. This is not realistic and in future analyses a frictional bond will be defined. Given the high vertical stresses above the pile cap (due to arching) this will inevitably lead to a significant change in the reinforcement tension at the edge of the pile cap.
The distribution of tension in the reinforcement is also affected by the subsoil. Figure 3 shows diagrammatically the effect of the subsoil, this behaviour has been observed in the FLAC. The tension is larger immediately adjacent to the pile cap. This behaviour has obvious implications for the incorporation of monitoring. Strain gauges are usually mounted mid way between pile caps (for example Jenner et al 1998) at this location it is likely that the strain gauges will underpredict the maximum strain.
This variability in tension is demonstrated in the results presented by Rogbeck et al (1998) for a piled embankment. An area of subsoil between pile caps was removed and replaced with a less stiff foam mattress. In the mattress area the strains adjacent to the pile cap were up to 4 times higher than midway between pile caps. It is possible that for the remainder of the embankment constructed on the subsoil the difference in strain between the pile caps and the mid point would have been greater.
Support System - Piles and Stone Columns
A variety of systems are available to provide support to the embankment. Systems commonly used include precast driven piles, vibro-concrete columns or stone columns. The piles have two significant effects; firstly their support of the embankment and secondly their ability to generate and dissipate pore pressures. Issues that need to be considered are:
Pile Stiffness - Stiffer piles will reduce settlement but will attract more load. Stone columns are less stiff and so would attract less load but would result in a larger surface settlement (although perhaps similar differential movement).
Pile Installation - If displacement piles are used, a large proportion of the excess pore pressures in the subsoil is likely to be due to pile installation. This will result in larger consolidation settlements than bored piles.
Drainage - If stone columns are used they would act as drains speeding up the consolidation of the subsoil.
In the analyses shown in the authors' response to Slocombe and Bells' discussion (GE March 1988) the influence of subsoil clearly has a major influence on the overall embankment response. However, the systematic inclusion of a degree of support from the subsoil in a design is not currently recommended.
The amount of consolidation settlement is difficult to quantify. This is due to the uncertainty in the initial excess pore pressure (due to pile installation and embankment loading), the consolidation properties of the subsoil, the change in loading from the embankment (as the soil consolidates and the reinforcement creeps) and the interaction between the subsoil and the piles.
This aspect forms a large part of the ongoing research and it is hoped that recommendations can be made for incorporation into new design methods.
The discussers suggest that conservative design methods lead to little savings over a reinforced piled slab. Although we have no comparative cost data we believe that the number of piled embankments being constructed must indicate that this method is less expensive. However, we agree that there are still savings to be made by optimising the design and the major potential beneficial factor is the support provided by the subsoil.
The paper and resulting discussions have clearly highlighted the complex nature of this apparently simple problem. There are many factors that influence the behaviour of the system and no single design method currently allows for all of these factors. We agree with the discussers that no design method is currently available to assess the magnitude of total and differential settlement. Although the authors are currently developing a design method for piled embankments, it is unlikely that this will be able to predict accurately the magnitude of movement. Given the tight tolerances for some schemes (for example the maximum differential movement of 1 in 1000 at the Second Severn Crossing) it is recommended that 3D numerical analyses are carried out to predict serviceability conditions.
The currently available design methods (with the exception of the Guido Method) are likely to provide conservative designs for the normal range of embankment geometries if used cautiously. The BS8006 design method has been calibrated against many constructed projects. Although it is tempting to allow for the beneficial effects of the subsoil, the authors would caution against incorporation of this beneficial effect in current design methods. The long term behaviour is currently allowed for in the FLAC analyses for by using a reinforcement stiffness applicable to the end of the design life and to assume that no support is provided by the underlying soil.
The authors agree that all design methods and analytical techniques should ultimately be assessed relative to appropriate case history data. The recent paper by Rogbeck et al (1998) may provide one such case history and will be back analysed by the authors.
Jenner, C G, Austion, R A and Buckland, D (1998). Embankment support over piles using geogrids. Sixth International Conference on Geosynthetics, Atlanta, USA.
Kempton, G, Russell, D, Pierpoint, ND, and Jones, CJFP. Two- and Three- Dimensional Numerical Analysis of the Performance of Piled Embankments. Sixth International Conference on Geosynthetics, Atlanta, USA.
Rogbeck, Y, Gustavsson, S, Sdergren, I and Lindquist, D (1998). Embankment support over piles using geogrids. Sixth International Conference on Geosynthetics, Atlanta, USA.