MANDOLINI 6.1 Introduction

Traditional design methods for piled foundations still concentrate on providing axial capacity from the piles to carry the total structural load. Such an approach gives no credit to the contribution of the raft and is

considered to be conservative. Moreover, it is adopted as a common practice by engineers in many countries and prescribed by the majority of existing codes and regulations.

Starting from the pioneering work by Burland et al.

(1977), in the last decades a large amount of research has been aimed to the use of piles to control average and differential settlement (respectively, settlement based design approach, SBD, and differential settlement based design approach, DSBD) of an unpiled raft whose bearing capacity is sufficient to carry the total external load with a reasonable factor of safety against failure. In other words, it could be said that the ‘piled raft concept’ has been conceived for fulfilling SLS requirements (‘piles as settlement reducers’), in some way implicitly assuming that the “raft ensures adequate bearing capacity, thus piles have to ensure only ade-quate increase of stiffness”.

If compared with the amount of research carried out on the behaviour of piled raft under service loads, there is no doubt that less attention has been dedicated by researchers to the interaction via soil between piles and raft when approaching failure.

Some recent results show how the matter is more complex as it appears, suggesting that, even in the case of settlement reducing piles, an assessment of the response of a piled raft at failure is suitable to ensure that satisfying SLS requirements does not compromise design requirements in terms of ULS.

6.2 Interaction between raft and piles at failure Depending on how piles are located underneath the raft, they could leave practically unchanged the bear-ing capacity of the unpiled raft (Q_UR) or determine a reduction of its potential contribution because inhib-ited by their presence. At the same time, piles failing in a group under a load Q_PG could reduce their bearing capacity when combined with a raft in contact with soil, for instance as a consequence of the inhibited relative pile-soil relative movement at shallow depth close to the raft; in some cases, they could increase their bearing capacity as a consequence of the sur-charge effects due to the contact raft-soil stresses.

In general terms, it could be said that the bearing capacity of a piled raft can be evaluated as:

Q_PR= αUR⋅ QR+ αPG⋅ QPG (1) where αUR and αPG represent respectively the factors affecting the bearing capacities of the unpiled raft Q_UR and of the pile group Q_PG, both of them convention-ally evaluated (for instance, for the pile group: Q_PG= η ⋅ n ⋅ QS, where η = efficiency at failure of the pile group made by n piles having a failure load Q_S).

With reference to the numerical results obtained by 3D FE analyses of vertically loaded piled rafts Figure 6. Total load-settlement behavior of the test piles.

resting on soft clayey soils, de Sanctis & Mandolini (2006) found that a factor FF can be introduced to better understand the interaction at failure of the two components (raft and piles):

FF

where A_G is the area occupied by the piles underneath the raft area A and s/d is the ratio between pile spac-ing and pile diameter.

Figure 7 groups the numerical results in terms of reduction factor αUR to be applied to Q_UR to give the contribution αUR ⋅ QUR of the raft at failure when combined in a piled raft. For all the analysed cases, it was found αPG∼ 1.

Data in Figure 7 have been reasonably fitted with a simple linear regression, thus suggesting the fol-lowing comments: (i) for the case of an unpiled raft (A_G/A = 0), αUR= 1 as expected; (ii) for the case of piles uniformly spread underneath the raft (A_G/A ∼ 1) at relatively small spacing (s/d ∼ 3), αUR∼ 0. It fol-lows that (A_G/A)/(s/d) ∼ 1/3 may be viewed as a criti-cal value for FF corresponding to the transition from a pile group behaviour (i.e., no contribution of the raft is allowed, αUR= 0) to a piled raft behaviour (i.e., the raft supplies a fraction αUR> 0 of its bearing capacity when unpiled).

It is interesting to note that Cooke (1986) sug-gested values for s ∼ 3 ⋅ d as that critical value of the spacing below which a pile group embedded in a clayey soil tends to exhibit ‘block’ mode of failure instead of individual pile mode of failure.

Putting together all the things, it could be said that for piles uniformly spread underneath the raft (A_G/A

∼ 1), the adoption of pile spacing ratio s/d < 3 yields to ‘block’ failure of the pile group preventing the raft to contribute; on the other hand, spacing ratio s/d > 3

prevents the pile group to fail as a ‘block’ making the raft able to transfer load directly to the soil.

Let us consider now the case of an unpiled square raft (width B = 17 m) at ground surface resting on a clayey soil (soil shear stiffness G = 10 MPa; und-rained shear strength c_u = 100 kPa; Poisson’s ratio ν = 0,2) loaded by an external total load Q = 50 MN.

The evaluation of failure load in undrained conditions with conventional bearing capacity theory yields to Q_UR∼ 178 MN, that means FSUR= QUR/Q ∼ 3,6.

The evaluation of the long term settlement with sim-ple elastic theory yields to w_∞,UR∼ 108 mm. Such set-tlements are considered not admissible (for instance, w_adm= 50 mm) and hence piles have to be added to reduce settlement.

If bored piles with length L = 30 m and diameter d = 1 are selected, the conventional approach for the evaluation of failure load of the single pile yields to a value Q_S∼ 4 MN (slim= α ⋅ cu, α = 0,35; plim= Nc ⋅ cu; N_c= 9). Assuming an efficiency of the pile group at failure η ∼ 0,7 and neglecting the contribution of the raft in contact with soil (i.e. assuming that all the load is transferred to the soil by only the piles), at least 6² piles at spacing s = 3 m are needed (QPG= 0,7⋅36⋅4 ∼ 100 MN) to ensure a factor of safety not lesser than 2. The corresponding settlements of the pile group, evaluated by the interaction factor method, yields to a long term settlement w_∞,PG∼ 39 mm.

According to Burland (2004), a structure, its foun-dation and the surrounding ground interact with each other whether or not the designers allow for this inter-action. In practice and looking at piled raft behavior, it means that although we decided to neglect raft con-tribution, it exists!

From quantitative point of view, the “true” fac-tor of safety of the piled raft can be evaluated by using eq. (1):

The evaluation of the settlement of the piled raft by the PDR method (Poulos, 2000) yields to w_PR∼ 40 mm.

The example show that the addition of the piles allow to fulfill the design requirement for which they have been added but, at the same time, they limited the contribution of the raft to about 20% of its poten-tial contribution, giving a resulting factor of safety decreased from the initial value for the unpiled raft FS_UR∼ 3,6 to FSPR∼ 2,8.

If only 4² piles at spacing s = 5 m are used, the efficiency at failure of the pile group can be assumed Figure 7. Relationship between αUR and FF.

0.0

to increase to about 0,8 and the following results Less piles more spaced slightly increase FS_PR leav-ing practically unchanged w_PR∼ 40 mm.

7 CONCLUSION

Even for those cases where piles are used to reduce settlements, their presence can affect the bearing capacity of the raft, giving a factor of safety of the combined piled raft smaller than that ensured by the raft when unpiled. Such findings suggest to evaluate always the available bearing capacity in order to check if the requirements fixed by Codes (when allowing innovative design approaches) are satisfied.

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