This study investigates the steady flow resulting from dewatering by a partially penetrating well in a confined aquifer with a cut-off barrier. By considering flow in both horizontal and vertical directions and incorporating the barrier and pumping well as flow boundary conditions, separate mathematical models are established for the inside and outside of the cut-off barrier. The interaction between these zones is ensured through continuous conditions along the opening of the two zones. A semi-analytical solution is derived for the problem using the finite Fourier cosine transform and boundary transformation methods. The effectiveness of the method is verified by comparing it with the finite element numerical results and pumping test data respectively. Based on the proposed solutions, we proceed to analyze the influence of some relevant factors: the extent to which the cut-off wall is embedded within the confined aquifer, the depth of the partially penetrating well, and the distance to the lateral head boundary. Results indicate that a greater depth of the cut-off wall leads to a reduced pumping rate requirement for achieving a desired drawdown of the confined water level within the excavation. According to the presented solution, placing pumping wells near the top of the confined aquifer in excavation dewatering projects can facilitate a faster reduction of the confined water head at the excavation bottom. Additionally, proximity of lateral head boundary could significantly impact dewatering, with closer boundaries reducing dewatering effectiveness due to improved aquifer recharge. Finally, the use of the Fourier method showcases impressive convergence properties in the approach presented in this study. The computed results maintain a high level of approximation quality, even with extremely coarse discretization.

For ground with trapezoidal distributed subgrade reaction coefficients caused by natural sedimentation, a calculation model for pile(wall) deflection deformation under lateral loads was established. Based on the theory of power series solution of differential equations, a power series solution for pile(wall) deflection deformation that considers the trapezoidal distribution of lateral loads and subgrade reaction coefficients was proposed. The power series solution can be degraded into the traditional K-method and m-method formulas for calculating pile(wall) deflection deformation. The results show that when the number of calculation terms of the power series solution is taken as 20, the maximum relative truncation error of the horizontal displacement is 0.19%, and the calculation accuracy can meet the requirements of theoretical analysis and engineering calculation. For long pile(wall) with a converted depth $\overline{h}$ greater than 5 m, it is suggested to calculate at 5 m. The analysis of engineering examples demonstrates the validity. The proposed power series calculation method solves the problem of pile(wall) deflection deformation with trapezoidal distributed subgrade reaction coefficients under lateral loads, which the traditional K-method and m-method cannot solve. Compared with the finite element method, the computational efficiency of the deterministic method is improved. Therefore, the proposed method can support the establishment of calculation methods for complex problems such as pile(wall) deflection deformation in multi-layered ground and anti-slide piles under local lateral loads.

This study addresses the early-age brittleness and performance limitations of sustainable cement soil. While prior works optimized the baseline compressive strength using recycled sand and nanoclay, the multi-scale synergistic effects of fibers and nanomaterials on the post-peak deformation remain underexplored. To address this gap, a composite modification system incorporating recycled sand, nanoclay, polypropylene fibers, and graphene derivatives was developed. The experimental program comprised standard specimen fabrication, early-age curing, and unconfined compressive strength (UCS) testing, supplemented by RBF neural network curve fitting and quantitative ArcGIS digital image processing of scanning electron microscopy (SEM) micrographs. The results demonstrate that optimizing the fiber parameters (0.6% content with 6 mm length) successfully increases the early UCS to 2263.2 kPa, which is further elevated to a peak of 2755.0 kPa upon co-incorporation with 0.05% small-sized graphene oxide. Correspondingly, a newly introduced ductility index quantitatively confirms that the single-fiber reinforcement yields an index of 1.93, which is further enhanced to 2.02 by the graphene composite system. Microstructure tracking and digital image extraction revealed that the SEM-derived surface porosity decreased significantly, exhibiting a clear inverse relationship with the macroscopic mechanical strength. These quantitative microstructural shifts confirm that graphene effectively filled micropores and reinforced the fiber–matrix interface, establishing a dense matrix network with enhanced interfacial bonding. This multi-scale approach offers a sustainable strategy for green geotechnical applications.