Contribution by T. W. Feng, Chung Yuan Christian University
It is interesting to note that the authors carried out laboratory dynamic compaction model tests with conical-bottom tampers. It would be more beneficial to the readers if the authors had explained in the paper the backgound to the use of a conical-bottom tamper in dynamic compaction. In this regard, it is helpful to point out a paper published in 2000 in Géotechnique by the discusser and co-workers1 on the same topic of conical-bottom tampers. The idea of using a conical-bottom tamper was explained in that paper. In principle, the partition of tamper impact energy into Rayleigh waves and body waves is better for a conical-bottom tamper than for a flat-bottom tamper. The discusser and co-workers have conducted laboratory dynamic compaction model tests using conical-bottom tampers with apex angles of 60°, 90° and 120°. It was our experience that the 90° conical-bottom tamper worked the best, regardless of the type of sands used in our model test programme. The 60° conical-bottom tamper penetrated excessively into the specimen. The 120° conical-bottom tamper created craters smaller than that created by the 90° conical-bottom tamper.
The cone angle used by the authors is equal to 180° minus the apex angle. For example, the 90° apex angle refers to a cone angle of 45°. The authors proposed determining the cone angle of the conical-bottom tamper according to the internal friction angles of the sands. However, judging from our experience, this may lead to a conservative design of the tamper. For a loose sand with internal friction angle of 30°, the cone angle is 30° and the apex angle is 120°. The efficiency of the 120° tamper is likely to be smaller than that of a 90° tamper. Furthermore, it should be simple and practical to build only a tamper with a proper apex angle for general applications. In this regard, the discusser would suggest that the 90° apex angle conical-bottom tamper be considered.
Authors' reply
The discusser proposes that the efficiency of the 120° tamper is likely to be smaller than that of a 90° tamper. The discusser's comments show that an intensive philosophical debate is going on as to whether or not to consider the effect of different components on tamper weight shape. The discusser suggests our agreeing that the 90° apex angle conical-bottom tamper be considered. However, it is as yet impossible to make such a general statement.
There are many factors that have a great effect on dynamic compaction efficiency. Two most important considerations regarding the applicability of dynamic compaction are the type of soil being densified and the in situ water content. Our experimental conditions considered only one type of granular soil and a constant water content. Thus we were not able to investigate the effect of different parameters on dynamic compaction efficiency using a conical-angle tamper. We did not propose a best shape for the tamper. It may not be possible to make such a statement with such limited information. The discussion shows that the utilisation of conical-bottom tampers requires more research, both experimental and numerical. However, our experimental study showed that consideration of the friction angle of granular soil, and therefore of its bearing capacity, would be useful for conical-bottom tamper efficiency, especially if depth is the most important issue for ground improvement requirements.
A conical bottom may be useful for different ground improvement projects. For instance, dynamic compaction has started to be used for abandoned mine remediation, in which the maximum depth of improvement is important. Thus, for this case, smaller angles would be more useful. However, crater area may be more important than crater depth for another project, so that a larger apex angle would be more practical. More examples can be given to explain that the most efficient apex angle is dependent on the project requirements and the soil condition.
As a result of many contributing factors, the efficiency of the tamper shape may change from project to project. Thus engineering analyses and evaluations of the different components are necessary before proposing a statement as concrete as that of the discusser. In order to fully understand the benefits of conical-bottom dynamic compaction, however, one must first investigate the effect of different contributors to and project requirements for the dynamic compaction process.
A comprehensive picture of the most efficient tamper shape for deep compaction is still largely obscure. Our paper attempted to develop a comprehensive understanding of the mechanisms contributing to dynamic compaction efficiency. However, further studies are needed to improve the dynamic compaction effectiveness.
