Predictive model and formula of jacking force has been well-established for circular pipe jacking in the past decades. However, the frictional mechanism of pipe–soil–slurry and jacking force prediction of rectangular pipe jacking has not well been understood. Nowadays, the rectangular pipe jacking is widely used, because of its over 20% larger effective usable area than that of circular pipe as underground facilities, with the same cross-sectional area. Nevertheless, the corresponding prediction models of thrust of rectangular pipe jacking are lacking. In order to further understand the frictional mechanism of slurry rectangular pipe jacking, five classical analytical calculation models have been proposed, considering the pipe–soil–slurry interaction, and prediction formulas are obtained. Then, 3D finite difference method was introduced to estimate the jacking force by using FLAC3D. Finally, three case studies have been carried out to validate the proposed models. The results show that the numerical and theoretical results have good consistency, and what is more, the measured jacking force can be well included within the ranges of analytical models presented in this paper, which can improve the thrust prediction of rectangular pipe jacking.

A fundamental challenge in reliability‐based geotechnical design is optimizing cost‐effectiveness while adhering to a predefined failure probability target. Traditionally, failure probability is assessed via Monte Carlo simulation (MCS), which, despite its accuracy, is often prohibitively time‐consuming and expensive. This scenario frames reliability‐based geotechnical design as a constrained optimization problem (COP) characterized by a low‐cost objective and high‐cost constraints. Recent advancements have seen the application of Gaussian process regression (GPR) enhanced evolutionary algorithms (EAs) for managing COPs where both objectives and constraints incur significant expenses. However, methodologies adept at handling COPs with inexpensive objectives yet costly constraints remain underexplored. This paper introduces a novel approach utilizing a GPR–based differential evolution (DE) algorithm designed specifically for COPs with this cost disparity. Here, GPR serves as a surrogate model to estimate the actual performance derived from MCS assessments. The innovative use of expected improvement (EI) as a selection criterion for potential solutions is a key feature of this method. EI quantitatively evaluates each candidate’s potential to enhance economic efficiency and safety reliability, effectively converting the COP into a single‐objective optimization problem (SOOP). We demonstrate the efficacy of our proposed GPR–based DE algorithm through a case study of the Sau Mau Ping rock slope in Hong Kong, highlighting the method’s ability to achieve superior accuracy and substantial computational savings.

Recent advancements in underground construction have led to the widespread utilization of pipe jacking. However, the engineering challenges posed by frozen ground in pipe jacking projects have not been extensively studied. This research aims to address the critical challenges linked to employing pipe jacking in frozen ground for underground construction. It is widely recognized that the accurate calculation of jacking thrust and mitigation of pipe–soil interaction plays a crucial role in determining the success or failure of pipe jacking operations. To explore these issues, this study conducted numerical simulations and comparative analyses, considering various factors such as soil properties, geometric dimensions, and burial depth, to assess their influence on jacking thrust. Additionally, the study also examines the freeze–thaw effect on concrete pipes and the injected lubricant. The results indicate that the numerical model, which considers the temperature effects and static friction instead of sliding friction, provides a more reliable estimation of jacking thrust in frozen ground compared to traditional theoretical models. Furthermore, the freezing point depression method was successfully employed in the development of an anti-freezing lubricant, which can effectively reduce pipe–soil interaction even at extremely low temperatures of up to −10 °C.