Boyan Sun

Rapid identification of contaminant source information is critical for solving sudden groundwater contamination events. This paper constructs a combined EnKF-SPSO algorithm based on the ensemble Kalman filter (EnKF) and survival particle swarm optimization (SPSO) algorithms to groundwater contamination source identification, which includes determining the location of the source, initial concentration, and emission time. The proposed hybrid architecture improves upon conventional single-algorithm approaches by decoupling the identification process into two stages. First, the EnKF searches for the contaminant source’s location, thereby reducing the search space. Next, the SPSO estimates the initial concentration and emission time within the reduced domain. This two-stage process effectively mitigates the curse of dimensionality often encountered in standalone optimization methods. We set up two solute transport scenarios with different numbers of contaminant sources to examine the effectiveness of the algorithm and compare it with the EnKF, particle swarm optimization (PSO), and SPSO algorithms. The results show that the EnKF-SPSO algorithm can identify the contaminant characteristics more accurately without falling into a local optimum, and the average relative error is less than 1%. In addition, the EnKF-SPSO algorithm, for cases with measurement errors, is highly reliable. The combined algorithm can provide technical support for groundwater contamination remediations, risk assessments, and liability determinations.

The determination of the optimal random field element (RFE) size is crucial in soil slope reliability analysis as it governs the trade-off between precision in failure probability calculations and computational efficiency. Given the substantial computational burden associated with smaller RFE sizes, studies on their impact on slope failure probability are scarce. This research examines the influence of RFE size on failure probability and safety factor, employing the Karhunen–Loève expansion to generate random fields and integrating the simplified Bishop method with particle swarm optimization (PSO) to assess slope stability. Through Monte Carlo Simulation (MCS), this study investigates the effects of the ratio of slope height to RFE size (H/D_e) on slope reliability metrics across two illustrative cases. Results reveal a notable influence of H/D_e on the distribution of safety factors (F_s) and failure probability (PF), with overestimation observed at smaller H/D_e ratios. When H/D_e exceeds 10 for Example 1 and 15 for Example 2, the F_s distribution patterns in both scenarios stabilize significantly, displaying minimal variability. The PF of Example 1 and Example 2 decreases with the increase of H/D_e and remains basically unchanged when H/D_e exceeds 10 and 15, respectively. Consequently, a recommended H/D_e ratio of 20 is proposed based on the analyzed cases, facilitating accurate calculations while mitigating computational overhead.

The entry and exit method is a simple and practical method to decide the critical slip surface of slope. Nevertheless, it has the drawback of sacrificing computational efficiency to improve search accuracy. To solve this problem, this paper proposes an improved entry and exit approach to search for the critical slip surface. On basis of the random fields produced by applying the Karhunen–Loève expansion approach, the simplified Bishop’s method combined with the improved entry and exit method is used to decide the critical slip surface and its relevant minimum factor of security. Then, the failure probability is calculated by conducting Monte Carlo simulation. Two instances are reanalyzed to validate the precision and efficiency of the method. Meaningful comparisons are made to show the calculating precision and calculating efficiency of the improved entry and exit method in searching for the minimum security factor of slope, based on which the effect of the reduced searching range on slope reliability was explored. The outcomes suggest that the approach offers a practical device for assessing the reliability of slopes in spatially variable soils. It can significantly enhance the computational efficiency in relatively high-computational precision of slope reliability analysis.

The entry and exit method is a simple and practical method to determine the critical slip surface of slope. However, it has the drawback of sacrificing computational efficiency to improve search accuracy. To solve this problem, this paper proposes an improved entry and exit method to search for the critical slip surface. Based on the random fields generated by using Karhunen–Loève expansion method, the simplified Bishop’s method combined with the improved entry and exit method is used to determine the critical slip surface and its corresponding minimum factor of safety. Then, the failure probability is calculated by conducting Monte Carlo simulation. Two examples are reanalyzed to verify the accuracy and efficiency of the proposed method. Meaningful comparisons are made to demonstrate the calculating accuracy and calculating efficiency of the improved entry and exit method in searching for the minimum safety factor of slope, based on which the effect of the reduced searching range on slope reliability was explored. The results indicate that the proposed method provides a practical tool for evaluating the reliability of slopes in spatially variable soils. It can greatly improve the computational efficiency in relatively high-computational accuracy of slope reliability analysis.