Brittle failure of fractured rock materials under quasi-static loading is characterized by strong suddenness and severe consequences, making accurate prediction of crack evolution and failure load critically important. However, conventional continuum mechanics-based methods encounter singularities when addressing discontinuities, while the widely adopted dynamic relaxation (DR) method within peridynamics is applicable solely to the continuous deformation stage. To address this limitation, this paper proposes a two-stage joint algorithm combining dynamic relaxation and conventional explicit analysis within the peridynamics framework. In this method, the DR method is employed exclusively during the continuous deformation stage before the onset of loading-induced bond failure, while the conventional explicit algorithm is activated to simulate the subsequent crack propagation process. The feasibility and stability of the proposed method are validated through the failure simulation of an L-shaped concrete plate. Subsequently, the quasi-static failure behavior of Brazilian discs with pre-existing central cracks and slope models containing steep-gently dipping pre-existing fissures is systematically investigated. For Brazilian discs, the influences of crack inclination angle and relative crack length on failure modes and bearing capacity are revealed. The numerical results are consistent with experimental observations. For the two specific slope models considered, the geometric configuration characterized by θ = 90°exhibits tensile coalescence failure, whereas that characterized by θ = 56°exhibits tensile–shear coalescence failure; both numerical results agree with the corresponding experimental observations. The findings demonstrate that the proposed joint algorithm combines the computational efficiency of dynamic relaxation during the continuous deformation stage with an explicit approximation of the quasi-static fracture process during damage evolution. This provides a simple yet effective numerical solution for quasi-static failure analysis of fractured rock materials.
To investigate the earth pressure acting on shield tunnel linings in longitudinally non-uniform ground under non-stationary hydraulic conditions, this study develops a nonlinear analytical framework considering the mobilized shear strength of unsaturated soils. Closed-form displacement fields induced by the ground loss are first derived using the complex variable method. The soil domain is then discretized. Deviatoric strain, mobilized shear strength, and strain energy contribution of each soil unit are determined through a nonlinear stress–strain relationship. An energy balance equation is established by equating accumulated strain energy to external work. The circumferential earth pressure acting on the lining and the corresponding stress release coefficient are accordingly obtained. The proposed method agrees well with centrifuge test data and numerical simulations. It can reasonably capture the continuous transition of earth pressures from the full overburden state to the loosening pressure state during construction. The stress release coefficient increases nonlinearly with the ground loss ratio. It rises rapidly at small deformation and then gradually approaches a stable level. A higher groundwater level significantly weakens the stress-release capacity of the ground. For a ground loss ratio of 0.5 %, the stress release coefficient decreases by about 25.7 % when the groundwater table changes from a depth of 0.8 h (h = 12 m) to the ground surface. The hydraulic parameters of unsaturated soils and soil type also exert strong control on stress-release behavior. Among the soils considered, clay shows the highest sensitivity, followed by silt, whereas loess and sand are much less sensitive. The proposed framework provides a rational basis for support pressure design of shield tunnels in complex hydraulic environments.
Global climate change and extreme precipitation events pose increasing threats to agricultural systems worldwide. However, existing studies often fail to integrate the synergistic effects of precipitation, neglect the role of transportation infrastructure, and rely on data with coarse spatial resolution. To address these gaps, this study develops a “climate–cropland–transportation” framework. By integrating high-resolution hourly precipitation data (0.1˚) and 30 m cropland distribution data, we quantified the thresholds, frequency, and intensity of extreme precipitation to construct a Cropland Extreme Precipitation Exposure (CEPE) index using the entropy weighting method. Four transportation accessibility scenarios—considering the presence or absence of expressways connecting prefecture- and county-level cities—were simulated to examine their spatial coupling with the CEPE. The results reveal pronounced spatial heterogeneity in CEPE across the study area. Rural population density and industrial structure exert nonlinear regulatory effects on cropland exposure to extreme precipitation. Extreme precipitation intensity peaks at moderate population levels, while areas where the primary industry accounts for 30–40% of the economy constitute a critical buffering zone. Geographically, croplands in southwest China remain highly threatened by extreme precipitation, whereas the exposure fluctuates considerably across the Huang–Huai–Hai Plain and the Northeast China Plain. Uneven transportation accessibility further amplifies these exposures, creating vulnerability traps in regions with high exposure but low accessibility, such as the Northeast China Plain. These findings offer valuable insights for developing targeted agricultural and infrastructure strategies to strengthen agricultural resilience under climate extremes.
In real-world scenarios, data are commonly represented in multiple views. Multi-view subspace clustering (MVSC) has attracted significant research attention owing to its capability to integrate complementary information across views while characterizing data structures through self-representation mechanisms. However, most existing MVSC algorithms exhibit two drawbacks: 1) They often overlook the negative impacts of redundant features, which not only increase data dimensionality but also introduce noise, adversely affecting the clustering results. 2) They are based on matrix self-representation, which inherently suffers from limitations in handling high-dimensional real-world data and fails to comprehensively capture the underlying cluster structures. Due to the varying dimensions among different views, tensor self-representation cannot be directly formulated. To address these two problems, we propose a multi-view subspace clustering algorithm that integrates tensor self-representation and feature extraction into a framework (JTSF-MVC). Specifically, JTSF-MVC utilizes the transformation matrices to extract discriminative features from the original data, while ensuring that all views have the same dimensionality. The transformed data for each view are stacked into a tensor. Subsequently, tensor self-representation can be successfully applied to this tensor to learn essential similarity relationships between samples. Furthermore, we propose an extended version (JTSF-IMVC) to tackle the challenging problem of missing multi-view data. To derive the optimal solution of the objective function, we employ the ADMM to optimize the proposed algorithms. Extensive experimental results on nine baseline datasets show that our proposed methods outperform their competitors. Our code is publicly available at github.com/ytccyw/JTSF-MVC.
