The heterogeneous hydraulic conductivity of a subsurface medium is vital to the groundwater flow and solute transport. Probability is efficient for characterizing and quantifying the field characterization of hydraulic conductivity. Compared with sandy mediums, silty clay is paid less attention to due to its low hydraulic conductivity. For long-term solute transport and seawater intrusion, the low-permeable medium is considered as a remarkably permeable medium. This study reports on a comprehensive investigation on the hydraulic conductivity field of the Ningchegu site, located east of Tianjin City of China. Four layers recognized by 52 boreholes, plain fill, continental silty clay, mud–silt clay and marine silty clay, were deposited from the top to the bottom. The hydraulic conductivities measured via permeameter tests ranged from 2 × 10⁻⁶ m/d to 1.6 × 10⁻¹ m/d, which corresponded to the lithology of silty clay. The magnitude and the range of the hydraulic conductivity increased with the depth. Five probability distribution models were tested with the experimental probability, indicating that a Levy stable distribution was more matched than the log-normal, normal, Weibull or gamma distributions. A simple analytical model and a Monte Carlo technique were used to inspect the effect of the silty clay hydraulic conductivity field on the statistical behavior of the solute transport. The Levy stable distribution likely generates higher peak concentrations and lower peak times compared with the widely-used log-normal distribution. This consequently guides us in describing the transport of contaminations in subsurface mediums.

The sphere target played a vital role in terrestrial LiDAR applications, and solving its geometrical center based on point cloud was a widely concerned problem. In this study, we proposed a newly finite random search algorithm for sphere target fitting. Based on the point cloud data and the geometric characteristics of the sphere target, the algorithm realized the target sphere fitting from the perspective of probability and statistics with the help of parameter estimation. Firstly, an initial constraint space was constructed, and the initial center and radius were determined by finite random search. Then, the optimal spherical center and radius were determined gradually through continuous iterative optimization. We tested the algorithm with the simulated and realistic point cloud. Experimental results showed that the proposed algorithm could be effectively applied to all kinds of point cloud fitting. When the coverage rate was bigger than 30%, the fitting accuracy could reach within 0.01 mm for all kinds of point clouds. When the coverage rate was less than 20%, the fitting accuracy can reach ±1 mm, although it was reduced to a certain extent.

During the implementation of the riprap project, the underwater migration process of the stones is quite uncertain because of its difficulty to observe. The process of stone transportation is discrete, which makes it unsuitable to be described by a continuous differential equation. Therefore, considering the distribution of stone jumping and waiting, a continuous-time random walk (CTRW) model is established. Based on the actual engineering data, five schemes simulate the one-dimensional motion of riprap underwater and further discuss the spatial distribution and particle size of the riprap. The results show that the CTRW model can effectively predict the riverbed elevation change behavior caused by the riprap project. The suitability of the model for the prediction of riprap movement decreases first and then increases with the increase in the selected width. This indicates that the randomness of the motion of the riprap causes the width of the observation zone to have a significant effect on the overall behavior of riprap movement. When the width is large enough, the influence of the randomness of the motion can be reduced by the average movement behavior within the observation zone. While the observation time of riprap movement is from a short to long time scale, the transport behavior changes from subdiffusion to normal diffusion behavior.

Due to human activities, the evolution of the lower reaches of the Yangtze River is complex, and the underwater terrain near the docks is varied. There may be serious erosion and sedimentation of the bank slope, which will affect the stability and cause engineering accidents. To explore the changes in underwater terrain and their impacts, taking a dock in Jiangsu Province in China as an example, a multi-beam bathymetry system is used to conduct full coverage measurement of the underwater terrain at the front of the dock. A comprehensive analysis method for underwater terrain is proposed from the perspectives of contour lines, cross-sections, etc., in order to monitor the changes in erosion and sedimentation in the dock area. Then, the impact of underwater terrain changes on the bank slope stability is explored by simulating the bank slope soil and the concrete pile foundation. Targeted engineering measures to ensure the stability and safety of the dock and bank slope are proposed. The methods and conclusions proposed in this manuscript, including underwater terrain measurement, analysis of the impact of underwater terrain changes on stability, and recommendations for related engineering measures, will help to ensure the long-term safe operation of docks. This research will be of great significance in reducing water conservancy accidents and promoting sustainable and efficient development of water resources.