Symmetry

The smearing effect during drainage board installation in soft soil foundation repairs can reduce permeability and compromise the surrounding soil’s structure, limiting the foundation’s consolidation efficiency. This study introduces a novel duckbill-type casing pile shoe with an axisymmetric geometric structure to address issues related to the stability and coating control of conventional pile shoes. A Coupled Euler–Lagrange (CEL) method is employed to develop a three-dimensional model for large-deformation penetration. Additionally, a new analytical framework for the pile shoe insertion and coating mechanism is established by modifying the circular hole expansion theory based on axial symmetry assumptions. This research systematically explores the effects of pile shoe groove curvature, penetration rate, and soil types on the smear zone’s extent. The findings indicate that the circumferential shear effect in the near-field soil intensifies with an increased penetration rate, leading to the expansion of both strong and weak smear zones. When the groove curvature is between 90° and 135°, the smear zone changes from a concentrated to a dispersed pattern, reducing local stress concentration. The extent of the smear zone is also influenced by soil types: ordinary clay exhibits the smallest smear zone, while silty clay demonstrates the greatest. The enhanced circular-hole axisymmetric expansion model shows excellent agreement with the CEL simulation results, confirming its effectiveness when soil strength factors and pile shoe geometry are taken into account. The results provide a theoretical foundation and numerical assistance for the design of pile shoe structures, anticipation of smearing effects, and optimization of drainage board construction in soft soil foundations.

Symmetry plays a fundamental role in the evolution of mining-induced stress fields and the deformation behavior of roadway surrounding rock. To improve control of roadway deformation under strong mining-induced disturbance, this study takes the 12 Upper 301 face at Buertai Coal Mine and investigates the deformation mechanism and corresponding control methods. Based on an analysis of in situ monitoring data, the key stratum responsible for energy accumulation in the overlying strata was identified. Based on the inherent symmetry of the longwall mining layout, a symmetric predictive model of overburden key-stratum abutment pressure is established, which reveals the spatially symmetric distribution characteristics of the mining-induced stress field. The accuracy of the theoretical model was further verified through a large-scale geomechanical similarity model test, which reproduced the fracture trajectory and stress evolution law of the overburden key strata. To mitigate strong mining pressure, a targeted hydraulic fracturing control technique aimed at specific overburden horizons was proposed and verified through field testing and application. Field monitoring results indicate that roof-to-floor convergence peaked at 235 mm, and rib convergence peaked at 115 mm. Compared with sections without hydraulic fracturing control, the surrounding rock deformation was reduced by 62.3% and 69.7%, respectively, demonstrating a significant pressure relief effect. This approach effectively ensured the roadway stability and enabled safe mining operations.

Severe floor heave in gate roadways under high-intensity longwall mining is primarily controlled by mining-induced stress redistribution. Abutment pressure is preferentially transferred through the coal pillar into the floor, accelerating floor instability. From the perspective of symmetry, mining disturbance breaks the original mechanical symmetry of the coal pillar–roadway system, resulting in asymmetric stress concentration and uneven floor heave. In this study, field monitoring and FLAC3D simulations were conducted for the 12 Upper 301 panel in the Buertai Coal Mine. The objectives were to quantify the sensitivity of coal-pillar loading and floor-heave response under stress redistribution, and to derive implications for pressure-relief design. Field monitoring indicates strong disturbance and large deformation: the maximum roof–floor and rib-to-rib convergences reached 1095 mm and 452 mm, respectively, accompanied by continuous growth of coal-pillar stress during mining. Numerical results show that increasing coal-pillar width enhances stress-bearing capacity and promotes a more symmetric stress distribution, thereby suppressing floor heave. In contrast, increasing the mining advance rate aggravates stress-field asymmetry and intensifies floor uplift. Greater burial depth further strengthens stress concentration and amplifies asymmetric deformation. Based on these findings, a roof-cutting pressure-relief scheme was optimized. This scheme aims to relieve and re-route the asymmetrically transmitted pillar loading. The optimal design adopts a roof-cutting length of 75 m and an angle of 30°, which reconstructs a more symmetric stress-transfer path; reduces the peak side abutment pressure to 8.72 MPa; and limits floor heave to 134.4 mm (control rate: 88.4%). Field application confirms the effectiveness of the proposed symmetry-based pressure-relief design.