Belled and multi-belled piles are cast-in-place piles with one or several bell-shaped enlargements. In this study, centrifuge model tests were conducted to explore the bearing mechanism of belled and multi-belled piles in loess area. It was found that both the bell shape forming and pile loading procedure lead to the compaction effect of soil adjacent to the pile which was shown intuitively as the mutation of axial force and side friction resistance at certain positions of pile shaft. The compaction effect due to the bell-shape enlargement transformed to the squeeze out behavior when the bell is oversize, with negative effects on the bearing capacity of piles. The com-paction effect due to bell tip stress together with the bell tip resistance strengthens the attenuation rate of pile ax-ial force. A stable relationship in the percentages of bell tip resistance, pile tip resistance and the upper load was also found at the later load stage of multi-belled piles. A settlement calculation formula for multi-belled piles was proposed based on Mindlin solution. Finally, the accuracy of the formula was verified by model test results. The method for predicting the ultimate bearing capacity of multi-belled piles was proposed, and it was verified by an in-situ worked-out example.

Data and features often determine the upper limit of results, so that feature engineering is an important stage of federated learning. The existing research schemes all carry out feature engineering based on publicly sharing data. One is plaintext data sharing, the other is ciphertext data sharing, but both types of sharing bring security and efficiency problems. To address these challenges, we propose a feature engineering framework based on Secure Multi-party Computation, which supports multi-party participation in feature engineering and confines feature data locally to ensure data security. Moreover, the computational efficiency of the core algorithm of the framework is also improved compared with the existing methods.

Data island effectively blocks the practical application of machine learning. To meet this challenge, a new framework known as federated learning was created. It allows model training on a large amount of scattered data owned by different data providers. This article presents a parallel solution for computing logistic regression based on distributed asynchronous task framework. Compared to the existing work, our proposed solution does not rely on any third-party coordinator, and hence has better security and can solve the multitraining problem. The logistic regression based on homomorphic encryption is implemented in Python, which is used for vertical federated learning and prediction of the resulting model. We evaluate the proposed solution using the MNIST dataset, and the experimental results show that good performance is achieved.