Role of modelling in the development of design methods for basal reinforced piled embankments

Role of Modelling in the Development of Design Methods for

Basal Reinforced Piled Embankments

C.R. Lawson

TenCate Geosynthetics Asia SdnBhd, Malaysia

Abstract:The paper details the role modelling (analytical, physical and numerical) has played in the development of design methods for basal reinforced piled embankments; specifically the level of embankment arching and the determination of the magnitude of the tensile loads in the basal reinforcement. The paper also reviews the major national design approaches describing how the different methods operate. Comparison of the different methods is discussed.

Keywords: Piled embankments, basal reinforcement, geosynthetics, arching, analytical models, physical models, numerical models.

1

INTRODUCTION

Basal reinforced piled embankments are used increasingly to ensure stability and prevent differential settlements from occurring in infrastructure projects. This problem commonly arises where it is necessary to abut new embankments against piled structures (bridges or other embankments) that don’t undergo settlements. The typical layout of a basal reinforced piled embankment is shown in figure1. The embankment loading is transferred to the pile caps directly and via the basal geosynthetic reinforcement, thus ensuring negligible loading directly on the soft foundation between the pile caps. The embankment loading is then transferred via the piles down to a firm stratum. Different types of piles and columns have been used for this technique including concrete piles, timber piles, concrete columns, stone columns, lime columns, etc.

Figure 1.Typical layout of a basal reinforced piled embankment.

The advantages of using this technique are that embankments can be constructed to any height, at any rate, without the subsequent effects of settlements and instability. Applications where this technique can be applied are approach embankments to a piled bridge structure, embankment widening over soft foundations, and foundations for back-to-back retaining wall structures.

To design basal reinforced piled embankments various failure (limit) modes are assessed for an adequate margin of safety. These possible failure modes encompass pile group capacity, pile group extent, local stability, overall stability, outward sliding, surface deformation and vertical load shedding

onto the pile caps. Of these possible failure modes, it has been the vertical load shedding onto the pile caps and the resulting tensile loads generated in the basal geosynthetic reinforcement that has proved the most difficult to assess accurately.

The vertical load shedding at the base of an embankment and the tensile loads generated in the basal reinforcement are the result of a complex interaction mechanism between the embankment fill, adjacent piles and pile caps, the soft foundation and the basal geosynthetic reinforcement, figure 2. The interaction between these components results in tensile loads being generated in the basal geosynthetic reinforcement which are then distributed onto adjacent pile caps.

Figure 2.Diagram showing complex interaction between embankment fill, pile caps, soft foundation and basal geosynthetic reinforcement.

There are four key aspects to the design of the basal reinforcement in piled embankments. These are (see figure 2):

The nature of the arching between adjacent pile caps and the determination of the unarched vertical stress acting on the basal reinforcement.

The resulting deflected shape of the basal reinforcement and the method used to determine the generated tensile loads.

The method by which the unarched vertical stresses over the plane area of the basal reinforcement are transferred by tensile loads to adjacent pile caps.

The role of foundation support and to what degree this can be relied upon in determining the tensile loads in the basal reinforcement.

This paper showshow the above four aspects have been approached in the design of basal reinforced piled embankments and the role modelling has played in the development of these design methods.

2

MODELLING APPROACH TO BASAL REINFORCED PILED

EMBANKMENTS

Analytical models have been used as the basis for designing the basal reinforcement in basal reinforced piled embankments. These analytical models have been reasonably supported by physical and numerical modelling. To simplify the analytical modelprocedure it is divided into two separate parts where the embankment arching analysis is de-coupled from the basal reinforcement tensile load analysis. While dividing the analysis into two separate parts (see figure 3) simplifies the analytical approach itdoes

ignore any direct interaction between the embankment fill and the reinforcement (other than the direct vertical loading).

Figure 3.The de-coupling of embankment arching from basal reinforcement tensile loads in analytical modelling.

When analysing arching in piled embankments (the first part of the analytical approach) it is imperative to recognise if it isa 2D (plane-strain) or a 3D condition as this affects the choice of model and the consequent loading magnitude significantly. The nature of the arching is dependent on the layout of the piled foundation. Sometimes, piles are connected to each other by concrete connecting beams for stability reasons, and in this case the arching and the loading on the basal reinforcement can be considered in 2D terms (e.g. see figure 4a). However, for the vast majority of cases, individual pile caps are located at the base of the embankments and this creates a 3D condition, and should be analysed by 3D means (e.g. see figure 4b).

The various embankment arching methods used in the analytical models (figure 3a) have normally been derived from 1-g physical modelling experiments. The early analytical embankment arching models, e.g. BS8006:1995, were adapted from the physical modelling of similar-structures (i.e. Marston, 1930 and Terzaghi, 1943) with the results modified to suit piled embankments; while the later arching models were derived directly from piled embankment physical model tests, e.g. Hewlett and Randolph (1988),Zaeske (2001) and Heitz (2006). Carlsson (1987), Low et al. (1994) and Horgan and Sarsby (2002) have developed 2D analytical arching models, while BS8006:1995, Hewlett and Randolph (1988) and Zaeske (2001) have developed 3D analytical arching models.

The different analytical arching models have normally been described in terms of a series of equations taking into account embankment fill/pile cap geometry and embankment fill type, e.g. Hewlett and Randolph (1988), BS8006:1995 and BS8006-1:2010. Alternatively, the unarched vertical stress (p’f

in figure 3a) has been expressed in terms of a “stress reduction ratio” or an “arching ratio”, which is the unarched vertical stress (p’f) divided by the average vertical stress at the base of the embankment ( H),

and shown in graphical form, e.g. EBGEO (2010), CUR (2010). Lawson (2001) has presented several of these analytical arching models in graphical form which makes a visual comparison easier.

The second partof the analytical model involves the determination of the tensile loads in the basal geosynthetic reinforcement. Here, it is assumed that the unarched vertical stress acting between adjacent pile caps (p’f in figure 3) is supported by the basal reinforcement causing it to deflect and generate tensile

loads, which are then transferred along the reinforcement to the pile caps. For ease of computation two assumptions have been commonly made. First, that the vertical loading is evenly distributed across the length of the deflected basal reinforcement (see figure 3b). Second, that this evenly distributed vertical

loading acts on a horizontal plane between adjacent pile caps (see figure 3b). These assumptions enable the deflected basal reinforcement to be analysed as a parabola, as shown in equation 1.

(

)

where, Trp = tensile load in the basal reinforcement at the edge of the pile caps; p’f = average unarched

vertical stress acting on the basal reinforcement; Ac = area coverage ratio of the basal reinforcement (see

figure 4); s = spacing between adjacent piles; a = size of pile caps; = strain in the basal reinforcement; J = tensile stiffness of the reinforcement.

The unarched vertical stress p’f in equation 1 may be considered a net value. If there is no

foundation support beneath the basal reinforcement then the value of p’f is the vertical stress caused by

the unarched fill in the embankment only. If foundation support is taken into account then this can be subtracted from the unarched vertical stress in the embankment to arrive at a net value of p’f to be used in

equation 1.

Figure 4.Area coverage ratio of the basal reinforcement for 2D and 3D loading cases.

The area coverage ratio Ac in equation 1is the ratio of the basal reinforcement surface area subjected

to the unarched vertical stress divided by that area of the basal reinforcement that transfers the tensile loads directly to adjacent pile caps. For the 2D plane-strain case, the tensile loads are transferred to the pile caps in the way shown in figure 4a – there is an equal length of cap (beam) support for an equal

width of basal reinforcement. Thus, in the 2D case, Ac = 1.0. For the 3D case, the tensile loads are

transferred to the pile caps in either of the assumed ways shown in figure 4b – the tensile loads being transferred via a relatively narrow pile cap width. Thus, in the 3D case Ac> 1.0. Figures 4b(i) and 4b(ii)

show how different design methods have approached the 3D loading case from the perspective of area coverage. The area coverage ratio relationship shown in figure 4b(i) results in a more conservative value than that shown in figure 4b(ii).

The parabolic formula shown in equation 1 relates the basal reinforcement tensile load Trpto its

strain . Here, the smaller the reinforcement strain, then the greater the resulting tensile load calculated (all other things being equal). Table 1 lists maximum reinforcement strain values for basal reinforced piled embankments from a number of sources. From these, it might be assumed that typical maximum reinforcement strains range between 3% and 6% (these values are also influenced by the type of reinforcement being used).It should be noted that a change in maximum reinforcement strain from 3% to 6% results in a 40% reduction in the basal reinforcement tensile load calculated using equation 1, so a proper assessment of reinforcement strain is important. Equation 2 also relates basal reinforcement tensile load Trp to its strain by means of its tensile stiffness J. By solving equations 1 and 2 solutions

are obtained for Trp, J and at different times.

Table 1.Maximum basal reinforcement strains from different sources.

Source Basis Values Boundary conditions BS8006-1:2010 Past experience 6% No foundation support

Chew et al. (2006) Large-scale physical modelling

4% No foundation support

Kempton et al. (1998) 3D numerical modelling 4% Dependent on reinforcement type, embankment geometry and nature of foundation support

EBGEO (2010) Past experience 6% Dependent on reinforcement type, embankment geometry and nature of foundation support

Halvordson et al. (2010)

3D numerical modelling 3% Dependent on reinforcement type, embankment geometry and nature of foundation support

2.2 Physical modelling

Relatively few physical model tests have been carried out on basal reinforced piled embankments, although those that have have varied in scale from small (e.g. figure 5a) to large (e.g. figure 5b). Physical modelling hasnormally formed the basis for the development of a specific embankment arching theory.

A summary of 3D 1-g physical modelling of piled embankments is listed in table 2. All the small-scale modelling approximates a 1:3 small-scale resulting in a model size around 1 m x 1 m. Sand has universally been used as the embankment fill because of its ease of placement and consistent properties, while a range of materials have been used to simulate the deforming foundation. Piles have been rigid inclusions of timber or steel. Depending on the investigation program either scaled geotextile or geogrid specimens have been used as the basal reinforcement or no basal reinforcement has been included. Where scaled basal reinforcement has been included various techniques have been employed to measure deflections, strains and tensile loads in the reinforcement.

Table 2.3D 1-g physical modelling of basal reinforced piled embankments.

Reference Model size Embankment Foundation Reinforcement Measurements Marston (1930)* Buried

conduits

Sand Compacted soil

Nil Deformations, loads Hewlett and

Randolph (1988)

1 m x 1 m Sand Foam rubber chips

Nil Deformations, loads Demerdesh

(1996)

1 m x 1 m Sand Foam rubber chips Scaled geotextile Deformations, loads, reinforcement strains Zaeske (2001) and Heitz (2006)

1.1 m x 1.1 m Sand Peat Scaled geogrid Deformations, loads, stresses, reinforcement strains

Britton and Naughton (2008)

1 m x 1 m Sand Trapdoor Nil Deformations, loads Chew at al.

(2006) and Le Hello (2007)

3 m x 5 m Sand Coarse sand, then removed Full-scale geogrid Deformations, loads, stresses, reinforcement strains van Eekelen et al. (2011) 1.1 m x 1.1 m Sand and granular 0-16 mm Soaked rubber foam Scaled geotextiles and geogrids

Deformations, loads, load distribution

piles-reinforcement-foundation, reinforcement strains *While Marston carried out 2D modelling of buried conduits (and not 3D piled embankment modelling), the results have been used in a 3D arching model for piled embankments; hence it is included here for completeness.

Small-scale 1-g physical modelling has been able to demonstrate the nature of the embankment arching reasonably well (or has it?). Marston’s modelling of buried rigid conduits resulted in the 3D arching approach adopted in BS8006:1995 (see Section 3.1). Hewlett and Randolph’s modelling resulted in the hemispherical vault arching approach (see Section 3.2). Zaeske’s (2001) and Heitz’s (2006) work resulted in the multi-shell arching approach (see Section 4.2). Slight modifications to this multi-shell arching approach is the result of the modelling of van Eekelen et al. (2011), while Britton and Naughton (2008) validated their critical-height arching approach using physical modelling. It is interesting to note that each researcher’s arching theory has been successfully “demonstrated” by the physical modelling carried out, and not the reverse.

The majority of model tests of piled embankments measured arching through a glass wall in the model, and some recorded the vertical deflection. Additionally, loads were recorded on the pile caps and, in some instances, vertical stresses were recorded within the model embankment fill. From these results the various arching theories were developed.

One of the major difficulties with small-scale 1-g physical modelling has been the scaling of the basal reinforcement and the subsequent measurement of reinforcement tensile loads and strains, Demerdesh (1996). Depending on how the modelling is performed, the properties of the basal reinforcement used in the 1-g model may have to be scaled in order to accurately reflect behaviour in a full-scale prototype. The scaling of the basal reinforcement can lead to complications with regard to the choice of the model reinforcement material suitable for the modelling tests. Further, the instrumentation of the scaled basal reinforcement may also be complicated due to the small-scale involved and the sensitivity and performance of suitable instrumentation. To date, the most sophisticated measurement of model basal reinforcement behaviour has been that of Zaeske (2001) and Heitz (2006) who used vertical

rod extensometers to record the deflected shape of the modelled basal reinforcement and strain gauges to record reinforcement strains; and that of van Eekelen et al. (2011) who used strain gauges, strain cables and a vertical liquid levelling system (for vertical deflections).

Large-scale physical modelling has enabled the accurate assessment of basal reinforcement loads and strains, albeit normally under extreme loading conditions (without any foundation support) – see figure 5b. Chew et al. (2006) report on such a series of large-scale physical modelling tests of extreme geometry withs/a = 5 and H/(s-a) 1.5 (wide pile cap spacings in combination with low embankment heights). The purpose of these tests was to observe the conditions at the onset of failure and to record the loads and strains in the system. Extreme loading was induced by removing the foundation material beneath the basal reinforcement (see figure 5b)and, later, removing some of the basal reinforcement also. It was observed that an arch formed for embankment height ratios H/(s-a) 1.0, while no arch formed for lower height ratios. The basal reinforcement supported the unarched fill in all cases. Maximum strains in the polyester basal reinforcement were around 4% (after the removal of the foundation material) with thehighest values occurred near the edges of the pile caps. In the centre of the reinforcement span strains were around 1% to 2%.

More recently, centrifuge modelling of piled embankments have been performed (Ellis and Aslam, 2009a and 2009b). The modelling results obtained basically supports those obtained from 1-g physical modelling but in a more simplified manner.

2.3 Numerical modelling

The earliest numerical modelling of basal reinforced piled embankments occurred in the late 1980’s (Jardaneh, 1988), however, the results were limited due to the nature of the modelling software available at that time. It wasn’t until the mid-1990’s that modelling software became sophisticated enough, e.g. FLAC3D (ITASCA, 1993), (and readily available computers became powerful enough) that basal reinforced piled embankments could be modelled with any degree of accuracy.

However, surprisingly, there have been only a relatively small number of real 3D analyses carried out on basal reinforced piled embankments. Most of the numerical modelling carried out has involved 2D plane-strain and axi-symmetric models whose results must be viewed with caution. Probably, the reason why this form of numerical modelling is common (even today) is because the modelling is easier and the costs are lower (c.f. 3D modelling).

While there are a number of 3D numerical modelling software in existence, not all appear suited to the modelling of basal reinforced piled embankments, and this may explain some of the variations in results obtained. Further, the choice of the constitutive soil model and the type of reinforcement elements can also affect results. Little comparative research has been carried out in this area.

Numerical modelling has been able to analyse in detail the behaviour of the basal reinforcement under load. It has been able to confirm that the basal reinforcement placed close to the tops of the pile caps behaves as a “tensioned membrane” transferring the unarched vertical embankment stresses through the plane of the reinforcement onto the pile caps. In cases where multiple reinforcement layers have been modelled, it has been the bottom reinforcement layer that has generatedmost of the tensile loads; the upper layers contribute minimally.

One advantage with current 3D numerical modelling software is its ability to determine the tensile load distribution throughout the basal reinforcement. Figure 6 shows the results of 3D numerical modelling carried out by the author showing the typical distribution of tensile loads in the basal reinforcement due to the unarched fill in the embankment above. The zones are plotted in terms of the percentage of maximum tensile load. High tensile loads occur near the pile caps, and these reduce to 40-50% at the midpoints between adjacent pile caps. In the centre of the piled area the tensile loads are relatively low, around 10-20% of the maximum. Thus, there is a wide distribution of tensile loads throughout the basal reinforcement. Similar results have been obtained by Halvordson et al. (2010).

The results of the 3D numerical modelling shown in figure 6 have significant implications with regard to the design of the basal reinforcement in reinforced piled embankments. First, any analytical design method must be able to calculate the maximum tensile loads occurring at the edges of the pile caps (and not just the overall average loads). Second, the high tensile loads at the edges of the pile caps indicate that the unarched embankment stresses are greater in these locations than elsewhere, and with

lower vertical stresses at the centre of the mid-span. This conflicts with existing analytical methods that represent the vertical stresses as uniformly distributed across the basal reinforcement (see figure 3b) or as an inverted triangle (see figure 13b). Third, these variations in tensile loads may make it possible to use reinforcement more efficiently by using stronger reinforcement in the vicinity of the pile caps and weaker reinforcement near the centre of the piled areas, e.g. Russell et al. (2003). Further research is warranted in this area.

Figure 6.Tensile load distribution in basal reinforcement using 3D numerical modelling.

3

THE BRITISH APPROACH

3.1 The original BS8006:1995 approach

The earliest basal reinforced piled embankment structures constructed in the UK was in 1982 (Reid and Buchanan, 1984). Because of its perceived advantages (being able to construct an embankment to any height at any rate without the problem of subsequentsettlements and instability) it was considered important to develop a design methodology that could determine the level of arching at the base of the embankment and the resulting reinforcement loads. This early approach (and later approaches) resulted in the development of two analytical models, with further support from physical and numerical modelling, to describe the arching at the base of the embankment and the tensile loads generated in the basal reinforcement.

In the 1980’s well-founded information on arching in embankments was sparse. Terzaghi’s trapdoor analysis (Terzaghi, 1943) was available, however, it was thought (at the time) that the approach of Marston (1930) dealing with embankment arching associated with the presence of positive projecting conduits (rigid pipelines and culverts) would be more appropriateto describe this specific application (much of this is contained in Spangler and Handy, 1973).

Marston carried out medium- and full-scale 1-g physical modelling, first with rigid conduits (Marston and Anderson, 1913), and later with semi-rigid conduits to develop a 2D arching relationship to describe the difference in vertical stress above the conduit compared to the average vertical stress at the same depth (Marston, 1930). This difference in vertical stress (arching) was expressed in terms of the problem geometry (described in terms of a/H in figure 7a) and an “arching coefficient” (Cc in figure 7a).

The arching coefficient was determined from an empirically derived relationship (from the 1-g physical modelling) based on the problem geometry and the rigidity of the conduits. For rigid conduits, Cc 1.95

H/a – 0.18, and this was considered the situation most closely resembling a (rigid) piled foundation

beneath an embankment. It should be noted that there has been a long history of the successful use of Marston’s formula in estimating the amount of arching across the top of buried conduits (e.g. Young and O’Reilly, 1983).

Figure 7. Arching analogy used in the original British approach to basal reinforced piled embankments.

John (1987) adopted Marston’s 2D arching approach and modified it to suit the 3D conditions considered appropriate for individual pile caps beneath an embankment. The resulting “3D” arching relationship is shown in figure 7b. The relationship for the arching coefficient Cc remains the same as

that described above for the 2D arching case. At the time, no modelling was carried out to verify the basis of this “3D” approach.

The 3D arching relationship shown in figure 7b was combined with a limiting embankment height concept (the embankment height above which all vertical loading is transferred directly to the pile caps) to generate two equations describing the unarchedvertical stress at the base of a piled embankment between adjacent pile caps – one equation for the case where the embankment height is greater than the limiting height and the other equation for the case where the embankment height is less than the limiting height. These two loading cases are contained in the relevant section dealing with basal reinforced piled embankments of BS8006:1995 the British Code of Practice for Reinforced Soil. To simplify the mathematics the loading on the basal reinforcement was assumed to be uniformly distributed between adjacent pile caps.

When applying this “combination” arching model it has been observed that for certain specific piled embankment geometries the arching model gave “unusual” results, however, for other geometries the results appeared consistent. Demerdesh (1996), using small-scale 1-g physical modelling, also demonstrated that the BS8006 method gave consistent results for a number of geometries, but also gave inconsistent results for certain geometries. Russell and Pierpoint (1997) have also pointed out the inconsistencies in some of the arching solutions given by BS8006:1995.

In an attempt to remove the inconsistencies in the original BS8006 arching equations Lawson (1995) produced a graphical solution (see figure 8) where the results were plotted in terms of an “arching ratio” which is the unarched vertical stress between adjacent pile caps divided by the average vertical stress at the base of the embankment. When the arching ratio = 1.0, there is no fill arched across the pile caps and the vertical loading is transferred 100% directly to the foundation. When the arching ratio = 0, there is 100% arching with no vertical embankment loading transferred to the foundation. Where inconsistencies were calculated in the BS8006:1995 equations, curve-smoothing was applied to generate the smooth curves shown in figure 8.

Figure 8. Graphical solution to the BS8006:1995 arching equations (After Lawson, 1995).

In the BS8006:1995 method it was considered that foundation support between the pile caps could not be relied upon in practice, and so this was excluded from the determination of the net vertical loading acting on the basal reinforcement. This has been considered a safe, conservative approach in Britain (and is still followed today).

The unarched embankment fill acting on the basal reinforcement was assumed to do so in a uniformly distributed manner, and a parabola relationship (see equation 1) was used to determine the tensile loads in the basal reinforcement. To ensure all vertical loads were transferred along the load-carrying elements of the basal reinforcement to the pile caps a conservative approach was taken with regard the area coverage ratio, figure 4b(i). While this resulted in the calculation of higher tensile loads in the basal reinforcement, compared with other approaches, it was considered that this was a safe approach, and would not significantly alter the total cost of a basal reinforced piled embankment structure.

It is important to note that the basal reinforced piled embankment design approach contained in BS8006:1995 has now been used in many countries throughout the world, and for many applications. While certain geometries may yield unusual arching values, and the determination of the basal reinforcement tensile loads may yield higher values (compared to other methods) the BS8006:1995 method has stood the test of time and has provided conservative (i.e. safe) designs.

3.2 The Hewlett and Randolph approach

Hewlett and Randolph (1988) carried out small-scale 1-g physical modelling of piled embankments (without basal reinforcement). Dry and moist sand was used as the embankment fill in the models with the foundation consisting of foam-rubber chips. The piles were represented by blocks of wood. The arching observed in the model tests could be represented by a series of hemispherical vaults (figure 9a). Using soil plasticity theory, analytical solutions were obtained for equilibrium conditions at the crown of the arch and on top of the pile caps shown in figure 9b. These were presented as sets of equations for both the 2D (plane-strain) case and the 3D (individual pile caps) case.

Comparison of the two British arching models (BS8006:1995 and Hewlett and Randolph, 1988) along with that of a comprehensive 3D numerical modelling study (Kempton et al., 1998) is shown in figure 10. The case of a “low-height” embankment (H/(s-a) = 1) is examined in figure 10a and that of a “high” embankment (H/(s-a) = 4) is examined in figure 10b. The results are plotted in terms of an arching ratio (p’f/ v’) and pile spacing to pile cap size ratio (s/a) in the same manner as the graphical

solution to BS8006:1995 shown in figure 8. For low-height embankments (figure 10a) there are significant differences in the calculated arching ratios between the three methods. BS8006:1995 calculates the least (conservative) values while Hewlett and Randolph (1988) calculate the most (conservative) values. The values of Kempton et al. (1998) lie midway in between. For high embankments (figure 10b) there are also discrepancies in the calculated arching ratios between the three methods, but not as great as for low-height embankments. As with low-height embankments, BS8006:1995 calculates the least (conservative) values, while Kempton et al. (1998) calculate the most

(conservative) values. The values of Hewlett and Randolph (1988) lie in between but track fairly closely to those of Kempton et al. (1998).

Figure 9. Piled embankment arching model developed by Hewlett and Randolph (1988).

Figure 10.Comparison of calculated arching ratios according to the various British approaches.

3.3 The current BS8006-1:2010 approach

The original BS8006:1995 has been updated and republished as BS8006-1:2010. In the revised section on basal reinforced piled embankments both the original BS8006:1995 (Section 3.1) and the Hewlett and Randolph (1988) (Section 3.2) arching methods are provided. The original BS method has been provided because of legacy and continuity requirements (it is well-known and well-used internationally), while the Hewlett and Randolph method has been added because it is considered to better represent the “real” 3D arching mechanism in piled embankments. No preference is given to either method in the Code, and the designer is left to choose a specific method. The author considers this a point of weakness because designers will inevitably choose the method that provides the most economical solution, i.e. the one that calculates the lowest unarched vertical stresses. If one looks at figure 10, the original BS8006:1995 method calculates the lowest unarched vertical stresses (the lowest arching ratios), therefore it could be assumed that designers would continue to use this method (as opposed to the Hewlett and Randolph method) as it calculates the most economical solution.

In BS8006-1:2010 the calculation of the basal reinforcement tensile loads is carried out in the same manner as the original BS8006:1995. Also, the same area coverage ratio value (figure 4b(i)) is used as

before. There is no allowance for foundation support in the calculation of reinforcement tensile loads as it is considered this cannot be relied upon in practice.

Even though there are now two arching models given in BS8006-1:2010, the calculation of the tensile loads in the basal reinforcement will still yield relatively high values (c.f. other modern design approaches). This is due to the use of a conservative arching method (e.g. the Hewlett and Randolph method), the adoption of a conservative area coverage ratio valueand that no foundation support can be taken into account in the basal reinforcement tensile load calculation. However, having said this, the design methods presented in the BS8006-1:2010 do have a long history of use.

4

THE GERMAN APPROACH

4.1 The “old” German approach

While accounts differ, the first basal reinforced piled embankment structures began to be used in Germany in the early1990’s. As was the case elsewhere, the perceived benefits of this technique made it an attractive, economic proposition.

To analyse basal reinforced embankments the arching model developed by Hewlett and Randolph (1988) (Section 3.2) was used to assess arching. The tensile load in the basal reinforcement was determined using the parabolic relationship in equation 1, using the reinforcement area coverage ratio shown in figure 4b(i). Some support from the foundation could also be taken into account in this early approach.

Combining the Hewlett and Randolph arching method with the parabolic tensile load relationship (equation 1), and using the reinforcement area coverage ratio shown in figure 4b(i), results in a very conservative calculation of basal reinforcement tensile load, especially for low-height embankments (H/(s-a) = 1).

4.2 The “new” German approach

The “new” German approach adopts the multi-shell arching theory proposed by Kempfert et al. (1997) (see figure 11). One of the rationales behind the development of this theory was that it gave less conservative arching values, especially for low-height embankments, than existing theories (Hewlett and Randolph, 1988, BS8006:1995) which were thought to be too conservative in Germany.

To develop this arching theory (figure 11) a series of instrumented 1-g physical model tests, at scale of 1:3, were carried out, Zaeske (2001). An analytical model, using plasticity theory, was developed to describe the arching effect. The vertical stress acting on the soft foundation between adjacent pile caps was given in the form of an equilibrium equation (Zaeske, 2001, and Kempfert et al., 2004). EBGEO (2010) provides a graphical solution to this arching equation.

To compare the arching results obtained using the new German approach with existing approaches covered already in this paper, figure 12 plots EBGEO (2010) arching results along with those shown in figure 10. For low-height embankments (figure 12a) the EBGEO (2010) arching results are significantly lower than the three previously presented results of Lawson (1995) - BS8006:1995, Hewlett and Randolph (1988) and Kempton et al. (1998). There appears to be only minimal consistency between the four methods for low-height embankments. For high embankments (figure 12b) the EBGEO (2010) arching results approximate closely those of Lawson (1995) - BS8006:1995, but are lower than those of Hewlett and Randolph (1988) and Kempton et al. (1998). While for high embankments there appears to be greater consistency between the methods, compared with low-height embankments, there is still significant differences in the determination of the magnitude of arching at different pile geometries.

Figure 12. Comparison of arching ratios calculated using EBGEO (2010) and other methods shown in figure 10.

In EBGEO (2010) the unarched vertical stress acting on the basal reinforcement is assumed to act on the truncated-diamond area shown in figure 13a. However, instead of converting this into an area coverage ratio (see figure 4b(ii)) to be multiplied by the average unarched vertical stress (p’f), it is

converted directly into a triangular vertical stress distribution acting between adjacent pile caps, figure 13b. With a triangular vertical stress distribution the deflected form of the basal reinforcement no longer takes the form of a parabola, and thus the simple parabolic relationship between reinforcement tensile load and tensile strain shown in equation 1 no longer applies. A more complex deflected shape has to be analysed in this case.

Figure 13.Vertical stress distribution acting on basal reinforcement (After Zaeske, 2001 and EBGEO, 2010).

EBGEO (2010) equates foundation support beneath the basal reinforcement in terms of a modulus of reaction by assuming it behaves as a Winkler foundation. The method of calculation of the modulus of reaction ksin EBGEO (2010) is quite precise and specific. This raises two important issues with this

approach. First, representing foundation support accurately in terms of elastic spring constants (the Winkler modulus of reaction approach) is doubtful due to the plastic and time-deformation nature of soft

foundation soils. Second, this precise and specific procedure given in EBGEO (2010) is difficult to reflect in practice (which can be much more variable and imprecise).

Zaeske (2001) developed and solved a differential equation that described the deflected basal reinforcement subjected to a vertical triangular load distribution and with foundation support provided by a Winkler foundation. A graphical solution has been developed for EBGEO (2010) and this is shown in figure 14. The chart provides values of basal reinforcement strain ( ) and tensile stiffness (J) in terms of resultant vertical load (Fk) and foundation modulus of reaction (ks). The tensile load in the basal

reinforcement can then be obtained by use of equation 2.

Figure 14.Determination of tensile load in basal reinforcement using EBGEO (2010).

5

THE DUTCH APPROACH

The Dutch approach (CUR, 2010) follows closely that of EBGEO (2010) – see Section 4.2. It adopts the German multi-shell arching theory to determine the unarched vertical stress acting on the foundation between pile caps. Thus, the arching ratio curves shown for EBGEO (2010) in figure 12 also apply to CUR (2010). The calculation of the tensile loads in the basal reinforcement also follows the method given in EBGEO (2010), including the allowance for foundation support based on a modulus of reaction value. The Dutch approach, along with the application of specific Dutch design partial factors, is described by van Eekelen et al. (2010).

It is interesting to note that several full-scale structures have been evaluated in The Netherlands, and while monitored case studies fall outside the subject of this paper, it is worthwhile mentioning them briefly as they shed light on the appropriateness of the different analysis methods. Van Eekelen et al. (2010) cite three monitored full-scale basal reinforced piled embankment experiments where it was demonstrated that embankment arching and basal reinforcement strains could be more-accurately described by the EBGEO (2010) method than other methods. This formed the majority of the rationale for adopting the EBGEO method in CUR (2010).

6

THE SWEDISH APPROACH

The earliest basal reinforced piled embankment structure constructed in Sweden was in 1972 (Holtz and Massarsch, 1976). A simple 2D analytical model was developed by Carlsson (1987) which assumed a constant arching angle of 75° within the embankment fill (see figure 15b). This original analytical model was not based on any results of physical modelling at the time. Rogbeck et al. (1998) modified this original model into a 3D form (an inverted, truncated pyramid) to take into account the situation where individual pile caps exist (figure 15a). The method adopts a critical-height approach (Hc in figure 15b),

above which any further embankment overburden is transferred directly to the pile caps. The unarched fill acting on the soft foundation between adjacent pile caps was expressed as a uniformly distributed vertical stress over the exposed area. Later, a slightly modified form of this 3D arching model was adopted by Nordic authorities (Svanø et al., 2000) – the arching angle was widened to include a range between 68° and 75°.Rogbeck et al. (2000) carried out 2D and 3D numerical modelling of several full-scale case studies as a means of validating the approach.

Figure 15.Piled embankment arching model developed by Carlsson (1987) and modified by Rogbeck et al. (1998).

Figure 16. Comparison of arching ratios calculated using Rogbeck et al. (1998) with other methods shown in figure 12.

To compare the arching results obtained using the Swedish approach with existing approaches covered already in this paper, figure 16 plots results using the Rogbeck et al. (1998)analysis along with those shown in figure 12. For low-height embankments (figure 16a) theRogbeck et al. (1998) arching results follow generally those of Hewlett and Randolph (1988) and Kempton et al. (1998), while being significantly more conservative than the other methods shown. For high embankments (figure 16b) the Rogbeck et al. (1998) arching results coincide with the other results at certain geometries, but the shape of the curve is quite different (and “flat”). For embankment arches assumed to have a constant arch angle (75° for the Swedish method) the arching ratio curves are relatively insensitive to pile cap spacings (s/a ratios) unlike the other arching methods. The arching ratio results shown in figure 16 confirm that there is little consistency between the different methods.

The deflected shape of the loaded basal reinforcement in the Swedish approach is assumed to form a parabola and is analysed using the relationship in equation 1. The 3D area coverage ratio used in equation 1 is that shown in figure 4b(ii). No allowance is made for possible foundation support in the calculation of tensile loads in the basal reinforcement as it was felt that this could not be relied upon in practice.

7

CONCLUSIONS

Basal reinforced piled embankments are an ideal solution where it is required to construct embankments on soft foundation soils to any height, at any speed, without the subsequent problems of instability and settlement.

A clear distinction needs to be drawn between the use of 2D (plane-strain) and 3D arching models in basal reinforced piled embankment design. Where individual pile caps are used for the piled foundations then it is clear that a 3D design approach is required. Applying a 2D approach to a 3D problem can significantly underestimate the unarched embankment loadings and basal reinforcement tensile loads, leading to unsafe designs.

Analytical models invariably divide the design of basal reinforced embankments into two parts. The first part deals with embankment arching across adjacent pile caps, while the second part deals with the conversion of the vertical unarched loads into a tensile load in the basal reinforcement. How this tensile load is transferred to the pile caps is also considered.

Small-scale 1-g physical modelling has been used to form the basis for the various analytical arching models developed. Where these models appear to break down are at embankment geometry extremes – at low height embankments and at large pile cap distances.

With the advent of powerful computer hardware and sophisticated 3D software, 3D numerical modelling of basal reinforced piled embankments has become a reality. No longer should 2D plane-strain and axisymmetric results be an acceptable substitute for the 3D condition being modelled in basal reinforced piled embankments.

There is little consistency between the different design approaches for the determination of arching ratio at the base of piled embankments. For low-height embankments this inconsistency is marked. For high embankments, while there is less variability, inconsistencies are still significant for some of the approaches. Because of this it is difficult to conclude which method is the most appropriate. Some of these methods have been used for many years in many full-scale structures and have demonstrated “safe” results (today, they are being labelled as “over-conservative”).

The deflected shape of the loaded basal reinforcement has been assumed to approximate that of a parabola for a number of the methods in order to simplify the mathematics. To meet the requirements of a parabola the vertical unarched stress is assumed to be uniform over the horizontal span between adjacent pile caps (in practice this is most-likely not the case). Where different loading conditions are applied to the basal reinforcement, such as, a non-uniform vertical load distribution and foundation support in direct contact below the reinforcement, the reinforcement no longer takes the deflected shape of a parabola and must be analysed differently.

The mechanism of how the vertical unarched stresses are transferred via the basal reinforcement to the pile caps is dependent on the structure of the reinforcement used and how it is laid out at the base of

the piled embankment. Normally, two layers of uni-directional reinforcement, laid orthogonally, are used as this meets the load-transfer requirements in a practical manner. The area coverage ratio (the plan area subjected to the vertical unarched stress divided by the area between adjacent pile caps) can be considered in terms of a double orthogonal layer or, alternatively, as a single-layer truncated-diamond area. The latter approach results in lower calculated tensile loads in the basal reinforcement.

The presence of foundation support can have a major impact on the magnitude of the tensile loads in the basal reinforcement. A conservative (i.e. safe) approach might be to ignore the effects of foundation support when calculating the tensile loads in the basal reinforcement, as the higher calculated tensile loads do not result in a significant cost increase in the overall piled embankment structure.

Using 3D numerical modelling indicates that the distribution of tensile load throughout the basal reinforcement is not constant, and is a maximum in the vicinity of the pile caps. However, current analytical design methods assume that the tensile load is constant throughout and is based on an average strain in the reinforcement. Failure to fully account for the interaction of the loaded and deflected basal reinforcement in contact with the unarched embankment fill, and soft foundation, leads to this discrepancy. For a safe design, it is important for any analytical design approach to replicate the real tensile loads occurring in the basal reinforcement in the vicinity of the pile caps. This may lead to a more conservative approach to the calculation of basal reinforcement tensile loads than what is given in some of the existing design approaches.

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