As a civil engineer myself, I can say that the answer to this question is not possible to answer in a general way, since it depends on the soil/bedrock characteristics at the site, and on environmental loading considerations (especially wind) specific to the site. On top of that, piles aren't the only kind of foundation design used- another common type is a "raft" which "floats" on the soil, distributing the load evenly across a wide area, in accordance with its bearing capacity. Choosing the optimal design for the foundation comes down to finding the least-cost way of meeting the design criteria, which is the usual engineering challenge. As the following paper describes, very tall buildings often use a combination of the raft and the pile approaches, appropriately known as a "piled raft."
"In the design of foundations for tall buildings, engineers face a challenging task as a conventional design approach may not be able to address all the key design issues. The foundation design team has to employ innovative approaches to tackle the problem. Due to the size of the tall building, it is necessary to design a cost-effective foundation system that meets the long term performance requirements... ..Piled raft foundations are a cost-effective form of foundation for tall buildings and have been extensively used by geotechnical engineers in the past two decades. For most piled raft foundations, the primary purpose of the piles is to act as settlement reducers. The proportion of load carried by the piles is considered to be a secondary issue in the design.
Unlike the conventional piled foundation design in which the piles are designed to carry the majority of the load, the design of a piled-raft foundation allows the load to be shared between the raft and piles and it is necessary to take the complex soil-structure interaction effects into account. The performance of a piled raft can be influenced by several factors such as the conditions of the supporting soil, relative stiffness between piles and soil, loading conditions, size and length of the piles, and pile arrangement. Therefore, the design has to take account of these factors to achieve the objective of economic construction with satisfactory performance.
In the design of foundations for tall buildings, design engineers have to understand the mechanism of load transfer from the raft to the piles and to the soil and then to address the following issues (Poulos, 2009):
· Ultimate capacity of the foundation subjected to vertical, horizontal and moment loading combinations.
· Influence of the cyclic nature of wind and earthquake on foundation capacity andmovements.
· Overall settlement of the foundation.
· Differential settlements, both within the high-rise footprint and between high-rise and low-rise areas.
· Load-sharing between raft and piles and load distributions along the piles.
· Possible effects of externally-imposed ground movements on the foundation system, for example movement arising from excavations for pile caps or adjacent facilities or movements arising from ongoing consolidation settlement of soft soils.
· Earthquake effects, including the response of the structure-foundation system to earthquake excitation and the possibility of liquefaction in the soil surrounding and/or supporting the foundation.
· Dynamic response of the structure-foundation system to wind-induced forces."
https://onlinelibrary.wiley.com/doi/abs/10.1002/tal.207
As specific examples, within the same paper, the 601 metre (m) tall Incheon [twin] Tower in Songdo, South Korea is designed as: "The tower foundation consists of a 5.5m thick raft supported by 172 no. bored piles socketed into the 'soft rock' stratum... ...The final design adopted a diameter of 2.5m as the pile diameter with a minimum socket length of two pile diameters into soft rock. The pile lengths vary from 36m to 66m, depending on the depth of the founding soft rock stratum. The raft is embedded into the ground with the base of the raft located at about 14m below the ground surface level." Similarly, the 1000+ metre tall Nakheel Tower in Dubai is designed as follows: "The foundation system consists of a raft with a thickness that varies up to a maximum of 8m supported by a total of 392 barrettes [piles]. The barrettes have sizes of 2.8m x 1.2m and 2.8m x 1.5m and extend to depths of 37m, 42m and 72m below the carbonate cemented siltstone where the base of the raft is to be founded."
So, at the end of a very long answer, the ratios you requested for these very tall buildings (as examples) would be a maximum pile length to building height of 66/601, or 0.1098:1, while the ratio for Nakheel is less than 72/1000, or 0.072:1.
