Reflection Positivity and Monotonicity

We prove general reflection positivity results for both scalar fields and Dirac fields on a Riemannian manifold, and comment on applications to quantum field theory. As another application, we prove the inequality $C_D \leq C_N$ between Dirichlet and Neumann covariance operators on a manifold with a reflection.Comment: 11 page

Contributions to Foundation Engineering in Geotechnique

Many of the important developments in the field of foundation engineering have been addressed in Géotechnique papers over the past 60 years. This paper briefly reviews some of these developments and related articles, particularly with respect to shallow and deep foundations. In the early days of Géotechnique, the power to perform sophisticated numerical analyses did not exist. Papers tended to focus on the solution of problems using simple models in which soil was modelled either as linear elastic or as perfectly plastic. Engineers sought simple closed-form analytical solutions for boundary-value problems. With the development of more powerful analytical, computational and experimental capabilities, and of more sophisticated pile installation technology (especially offshore), more recent papers have explored much more sophisticated approaches to a range of foundation problems, striving to achieve more realistic representation of working conditions. Géotechnique papers have attempted to solve the problems faced by the foundation engineering industry, with a strong emphasis on the underlying science; as a result, these papers have played a key role in the advancement of both the science and its applications in our discipline

Pile setup in sand – the "PAGE" joint industry project

The reliability of long-term axial capacity predictions for large, offshore-scale, piles is uncertain. Current databases of static load tests include very few entries with diameters ≥ 1m, and none >2m. Also, most of the available tests were conducted at relatively early ages after driving. The PAGE Joint Industry Project addressed this knowledge gap by collating and analysing dynamic driving data from 25 offshore piles with 1.6 to 3.4m outside diameters and contrasting these with dynamic re-strike tests conducted between 1h and 1 year after driving. Systematic signal matching was performed with two independent codes that applied different soil models and the outcomes were compared with predictions from modern CPT-based static capacity design methods. Additional supporting analyses were performed on other piles, where static and dynamic tests had been conducted, to help assess the relationships between statically and dynamically measured resistances. Piles with 0.3 to 3.5m outside diameters followed broadly common trends over the first 30 days after driving, with shaft capacities approximately doubling. While smaller (<1m) diameter piles driven at onshore/nearshore sites display marked further capacity growth, larger offshore piles showed little additional capacity gain after 30 days. The CPT-based Unified offshore pile design method offered conservative predictions for long-term shaft resistance, while no bias was apparent with the ICP-05 approach. An inverse relationship was identified between long-term shaft setup and diameter, which is ascribed to enhanced dilatancy applying at the pile-sand interface. The base capacities interpreted from dynamic analyses consistently fell far below the monotonic loading capacities predicted by current design methods and showed no significant trend to increase over time