The authors would like to thank the discussers for their interest in the paper. The authors agree that to validate fully any analytical procedure it is necessary to calibrate against data from real construction projects. However, the purpose of the paper was to compare various design methods with more rigorous numerical analyses since numerical analyses may be used to model the assumptions inherent in each of the design methods. Four design methods were considered; BS8006, Terzaghi, Hewlett & Randolph and Guido.
The paper confirmed the inconsistency of current design methods which has led to the disparity in the amount of reinforcement used in construction. The Second Severn Crossing and A13 were used as examples of similar embankments where there was a significant difference in the amount of reinforcement.
The discussers have questioned the applicability of the numerical analyses presented. In response the authors would like to provide more details of the numerical analysis procedure, discuss the Guido design method and present results of additional analyses of the SSC.
The soft subsoil between piles was not modelled in any of the analyses presented. This approach was adopted since it directly simulates the assumptions in all four design methods. As demonstrated below, it is this assumption, and not the other small differences between the analyses and the real construction, that leads to the large predicted deformations.
The discussers question the use of the 120 year design stiffness used in the analyses. This value of stiffness allows for the long term creep of the reinforcement and is therefore used in design. If a shorter design life is specified then a higher stiffness can be used.
For all analyses the reinforcing material was modelled at the base. This was done to allow comparison between design methods.
Guido Design Method
The research carried out by Guido was for footings founded on granular material with layers of reinforcement. The authors are unclear how this research can be directly applied to piled embankments. As the discussers state 'when assessing the validity of various design approaches, proven construction work must surely provide the yardstick for judgement', this statement must also apply to experimental work and using models of footing to represent piled embankments does not appear reasonable.
The Guido design method predicts much lower reinforcement forces than any of the other design methods or the numerical analyses. These forces appear to be unrealistically low. The assumption that the reinforcement increases the angle of friction in the fill to 45 does not seem sufficient to reduce the reinforcement forces to such low values. In any case it is likely that the peak angle of friction for a well compacted well graded fill would be 45 even if reinforcement were not included. Previous two- dimensional analyses, carried out by the authors to understand the mechanism of arching, imply that increasing the angle of friction of the fill above 30 has little effect on the performance of the piled embankment. If the authors have misunderstood the application of the Guido design method any additional information would be welcomed.
The discussers state that for the SSC the Guido design concept was subjected to two dimensional axisymmetric and plane strain analyses. Figure 1 shows the effect of these geometric assumptions. Plane strain assumes that the reinforcement only spans in one direction, Figure 1a. Axisymmetry again assumes spanning in one direction but radially, Figure 1b. The authors suggest that, while these analyses may give some indication of the mechanisms involved, two dimensional models have considerable limitations for validating the design concept. The true behaviour is shown in Figure 1c and is the basis of the three dimensional analyses presented. Comparison of two and three dimensional analyses are presented in Kempton et al (1998).
To provide further information to answer the discussers queries, results from two additional analyses of the SSC, summarised in Table 1, are presented.
The first additional analysis (SCC2) has two layers of reinforcement separated by 300 mm, as actually used at the SSC. The results in terms of settlement and reinforcement force are compared with the original analysis (SCC1) which has a single layer of reinforcement, Figure 2. The axial stiffness of each of the two layers was modelled as half that of the single layer in analysis SSC1. It can be seen that the average reinforcement force in each layer reduces by around 40% but the maximum displacement increases. This is because the lower reinforcement picks up proportionally more load than the upper reinforcement. Clearly the inclusion of multiple layers of reinforcement does not significantly affect the overall response.
The second additional analysis (SCC3) includes the subsoil between piles. A low, but realistic stiffness (E=0.5 MPa over a layer 3 m thick), is given to the subsoil as shown in Figure 3. The reinforcement force and fill settlement are again compared with the original analysis. It can be seen that the reinforcement force and fill settlement reduce substantially, to values close to those actually observed. The shape of the deformed reinforcement is modified with much higher strain in the reinforcement adjacent to the pile cap. Analyses were carried out which showed that the displacement and reinforcement force are sensitive to the stiffness of the subsoil.
The two additional analyses clearly demonstrate that the much lower settlement observed at the SSC is due to load being carried by the soft soil between piles and not due to the two layers of reinforcement.
The paper reported on the first phase of an ongoing research pro- ject. The first phase was specifically aimed at comparing design meth- ods with a more rigorous analytical tool. The work was published ahead of the remainder of the research in an attempt to clarify the design meth-ods currently in use. One of the most important outcomes of the analyses is that there is a significant difference in the reinforcement loads predicted by each of the design methods for the same embankment geometry.
The Guido design method predicts the lowest reinforcement loads for all practical pile embankment geometries. The authors believe that the Guido design method is unrealistic and should not be used.
The authors agree that the SSC behaved acceptably but believe that the acceptable behaviour is due to significant embankment loading being carried by the subsoil between piles. The load carrying capacity of the soil will change with time as the soil consolidates and the reinforce-ment creeps and is difficult to quantify reliably.
In view of the discrepancies shown in the available design methods, the authors stand by the statement that, currently the only reliable approach to design is by three dimensional numerical analysis.
If minimal reinforcement is to be used, the load carrying capacity of the foundation material must be determined and the long term deformation should be assessed. Further research is currently underway to quantify these aspects and it is intended that analyses will also be carried out to validate the numerical analysis with real construction projects.