Piled Raft Foundations 1 Design Principles

A piled raft takes into account the contribution of both the piles and the cap acting as a raft footing in carrying the imposed load. Poulos (2001a) summaries the different design philosophies for piled raft foundations :

(a) Piles are mainly designed to take up the foundation loads and the raft only carries a small proportion.

(b) The raft is designed to resist the foundation loads and piles carry a small proportion of the total load. They are placed strategically to reduce differential settlement. (c) The raft is designed to take up majority of the foundation

loads. The piles are designed to reduce the net contact pressure between the raft and the soils to a level below the pre-consolidation pressure of the soil.

Piled raft foundation has received considerable attention overseas. It has not been used in Hong Kong but the current practice of ignoring the contribution of pile cap in contact with the ground can be viewed as a conservative simplification of design philosophy (a) above.

7.6.3.2 Methodologies for analysis

The settlement analysis of a piled raft foundation can be based on relatively simple methods or complex three-dimensional finite element or finite difference analyses. Fleming et al (1992) presented a simple method of analysing the combined stiffness of the raft and the piles, which allows for interaction between the piles and the raft (Figure 7.13). The effect of alternative piling layout on foundation settlement can be assessed. The interaction factor approach discussed in Section 7.5.1.5 can be used (Poulos & Davis, 1980). For most practical problems, the influence of pile cap contact on the overall foundation stiffness is not significant at working condition.

Other simple analytical methods include methods suggested by Burland (1995) and Poulos (2001b). The Burland method is suitable for piles that are designed as settlement reducers. The raft is designed to take a portion of the foundation loads such that the settlement of the raft itself is within the acceptable limit of the structure. An adequate number of piles would then be designed to carry the remaining foundation loads. The geotechnical capacity of the piles is fully utilised at the design load. The settlement of the piled raft can be estimated based on the method suggested by Randolph (1994).

In Poulos' method, the vertical bearing capacity of a piled raft is estimated by : (a) taking the sum of the ultimate capacity of the raft and all

For a piled raft where the raft bears on a competent stratum, the approach of combining the separate stiffness of the raft and the pile group using the elastic continuum method is based on the use of average interaction factor, αcp, between the pile and the piled raft (or cap).

The overall foundation stiffness, Kf, is given by the following expression :

Kf = Kg + Kc (1 - 2αcp) 1 - αcp2 Kc Kg

The proportion of load carried by the pile cap (Pc) and the pile group (Pg) is given by :

_P Pc

c + Pg =

Kc(1- αcp)

Kg + Kc (1-2αcp)

Legend :

Kg = stiffness of pile group = Rg np Kv G = shear modulus of soil

Kc = stiffness of pile cap = 2G A_{I (1-ν}cap s)

αcp = average interaction factor = _{ln (r}ln (rm/rc) m/ro)

rm = radius of influence of pile ≈ length of pile ro = radius of pile

Rg = stiffness efficiency factor for pile group

(Section 7.5.1.6) D = pile diameter

Kv = stiffness of individual pile under vertical

load L = length of pile

νs = Poisson's ratio of soil Acap = area of pile cap

np = number of piles

I = influence factor, see Poulos & Davis

(1974) or BSI (1986) rc = equivalent radius of the pile cap associated with each pile = A_πncap

p

Figure 7.13 – Analysis of a Piled Raft Using the Elastic Continuum Method (Fleming et al, 1992)

1 2 4 6 8 10 0 0.2 0.4 0.6 0.8 1.0

Poulos & Davis (1980) Approximate analysis by Fleming et al (1992) L/D = 25 (νs = 0) L/D = 25 (νs = 0.5) L/D = 10 (νs = 0.5) rc ro Kg Kf

(b) taking the ultimate capacity of a block containing the piles and the raft, plus that of the portion of the raft outside the periphery of the piles, whichever is less.

The settlement behaviour is predicted by methods given in Poulos & Davis (1980). The load sharing between the piles and the raft is given by Randolph (1994).

There are other computer-based analyses based on simplified models (Poulos, 2001b). One of these models simulates the raft as a strip in one dimension and the piles as springs. Allowance is made for the interaction between various components, such as pile-pile and pile-raft elements. Such a model does not consider the torsional moments within the piled raft and may give inconsistent settlement at points where strips in the orthogonal directions have been analysed.

Another simplified model is to represent the raft as an elastic plate supported on an elastic continuum and the piles are modelled as interacting springs (Poulos, 1994). More rigorous solutions can also be carried out with three-dimensional finite difference or finite element analyses, e.g. the work of Katzenbach et al (1998).

For simplicity, most numerical analyses assume a uniformly distributed load over the piled raft. Such an assumption may not be correct since the pattern of the loading depends upon the structural layout and the piles. This may affect the local distribution of bending moment and shear force in the piled raft, particularly at locations subject to concentrated loads. Based on elastic theory, Poulos (2001a) proposed simple methods for determining bending moment, shear force and local contact pressure due to a concentrated column load on a piled raft. Where a sophisticated solution is required, a finite element mesh corresponding to the layout of columns, walls and piles may be necessary.

Poulos (2001b) found that simple methods could give reasonable accuracy in predicting settlement. An exception is the analysis using two-dimensional plane-strain method that can over-predict the settlement of the foundations. This could be attributed to the inherent nature of the plane-strain solution, which is not suitable for modelling non- symmetrical square or rectangular raft foundations.

Prakoso & Kulhawy (2001) proposed a simplified approach for designing the preliminary configuration of a piled raft. This approach assumes that the piles are used as settlement reducers. The deflected shape of the raft is first estimated to facilitate the selection of size of the raft and the ratio between the width of the pile group and the pile depth. Design charts are developed to evaluate the bending moment of the raft and the proportion of foundation load taken by the piles. This method may overestimate the average settlement in most cases and underestimates the differential settlement. It has better accuracy in estimating pile loads and the bending moments in the piled raft.

7.6.3.3 Case histories

Field measurements of the load taken by the raft and the piles at working conditions are summarised by Hooper (1979) and Cooke (1986). These suggest that the ratio of load in the most heavily loaded piles in the perimeter of the group to that in the least heavily loaded

pile near the centre could be about 2.5. Leung & Radhakrishnan (1985) reported the behaviour of an instrumented piled raft founded on weathered sedimentary rock in Singapore. The load distribution between the raft and the piles was found to be about 60% and 40% respectively at the end of construction. The measured raft pressures were highest below the centre of the raft. However, the degree of non-uniformity of the applied load is not known.

Radhakrishnan & Leung (1989) reported, for a raft supported on rock-socketed piles, that the load transfer behaviour during construction differed from the behaviour during the loading test, with less shaft resistance mobilised over the upper three diameters of the pile shaft under construction load. It was postulated by Radhakrishnan & Leung (1989) that the presence of the rigid pile cap might have inhibited the development of shaft resistance over the upper pile shaft. The end-bearing resistance mobilised under long-term structural loads was also noted to be significantly higher than that under the pile test. This may be due to group interaction effects or creep of the concrete. To a certain extent, the behaviour will also be affected by the ground conditions of the test pile site.