The Richards equation has high plasticity and compatibility. Compared with other curve equations, it has higher applicability and accuracy in describing S-shaped curves. It can describe the changes in the initial growth stage, rapid growth stage, and stable growth stage of organisms well and reflect the slow-fast-slow change characteristics of growth. In this paper, the Richards model is introduced into the settlement deformation prediction of loess-filled foundation. Taking a high-loess fill site in northern Shaanxi Province as an example, continuous settlement deformation monitoring is carried out for the filling during the project operation period, and the settlement characteristics of a loess-filled foundation are studied using the monitoring results. It is considered that the settlement deformation curve of a loess-filled foundation has similar characteristics; that is, its deformation increases slowly in the early stage, rapidly in the middle stage, and is basically stable at a fixed value in the later stage. Its cumulative deformation time history curve is a smooth S-shaped curve, and the cumulative settlement increases with time and tends to converge. Analysis shows that the time history curves of cumulative settlement, the settlement deformation rate, and the acceleration of loess foundation filling are highly consistent with the Richards model. Compared with the modified exponential model and hyperbolic model, the predicted results are closer to the measured results; that is, the Richards growth model can be used to predict the settlement deformation of a fill foundation.

For main engine changes, shafting torsional vibration of an exported VLCC tanker must be analyzed carefully. With the transition matrix method, the vibration models for the vessel with two different propulsion systems are made. The calculated results show there are forbidden rotated zones which are near to the vessel sailing speed, some necessary measures must be taken to make the forbidden rotated zones change in order that the vessel shafting system is to run safely in the long term instead of main engine changes.

To improve the seismic connectivity reliability (SCR) analysis efficiency of water distribution systems (WDS) based on Monte Carlo (MC) simulation, the quasi-Monte Carlo (QMC) method sampled by a low-discrepancy sequence is applied. Furthermore, a parallel algorithm combined with the breadth-first search algorithm for SCR analysis of WDS based on the QMC method and Compute Unified Device Architecture (CUDA) platform was proposed. A city WDS was taken as a computational example, the accuracy and efficiency of the traditional MC algorithm and parallel algorithm were compared, and the influence of the Sobol sequence and pseudo-random number sequence was analysed. The analysis results show that when 1,000,000 simulations are performed, the maximum error of the calculation results of the two methods is 0.2%, and the parallel method can obtain a six-fold speedup ratio compared with the serial method, indicating that the proposed parallel method is correct, meets the accuracy requirements, and helps to improve the SCR analysis efficiency. When the number of simulations is the same, the simulation results based on the Sobol sequence are more accurate than those based on the pseudo-random number sequence. The proposed parallel method also achieves a good acceleration effect in the SCR analysis of large-scale WDS.

Enhancing the seismic resilience of urban water distribution networks (WDNs) requires the improvement of both earthquake resistance and rapid recovery capabilities within the system. This paper proposes a multi-objective method to enhance the seismic resilience of the WDNs, focusing on system restoration capabilities while comprehensively considering the hydraulic recovery index, maintenance time, and maintenance cost. The method utilizes a random simulation approach to generate various damage scenarios for the WDN, considering pipe leakage, pipe bursts, and variations in node flow resulting from changes in water pressure. It characterizes the functions of the WDN through hydraulic service satisfaction and quantifies system resilience using a performance response function. Additionally, it determines the optimal dispatch strategy for emergency repair teams and the optimal emergency repair sequence for earthquake-damaged networks using a genetic algorithm. Furthermore, a comprehensive computational platform has been developed to systematically analyze and optimize seismic resilience strategies for WDNs. The feasibility of the proposed method is demonstrated through an example involving the WDN in Xi’an City. The results indicate that the single-objective seismic resilience improvement method based on the hydraulic recovery index is the most effective for enhancing the seismic resilience of the WDN. In contrast, the multi-objective method proposed in this article reduces repair time by 17.9% and repair costs by 3.4%, while only resulting in a 0.2% decrease in the seismic resilience of the WDN. This method demonstrates the most favorable comprehensive restoration effect, and the success of our method in achieving a symmetrically balanced restoration outcome demonstrates its value. The proposed methodology and software can provide both theoretical frameworks and technical support for urban WDN administrators.