Search Results (282)

This paper introduces a q-deformed extension of the Lindley distribution. This extension is obtained by replacing the classical exponential with the q-exponential function from Tsallis non-extensive statistical techniques. This transformation offers more control over the tail behavior of the distribution, providing a transition between exponential and power-law decay patterns. Such flexibility is particularly useful when modeling right-skewed data with excess kurtosis, where classical models may not adequately describe heavy-tailed and highly skewed data. We derive several key properties, including the quantile function, expressed by the Lambert–Tsallis function $W_q$, the raw and incomplete moments, the probability-weighted moments, and the Tsallis entropy. The distribution of order statistics is also investigated. For parameter estimation, we employ several frequentist methods and conduct extensive Monte Carlo simulation studies to assess and compare their performance. Finally, applications to real-world datasets show that the q-deformed Lindley model is practically superior and more flexible than the classical Lindley distribution and other well-known models. Full article

The deep foundation pit excavation of subway will cause horizontal displacement, uneven settlement and other adverse effects on the adjacent shield. The use of servo steel strut has a certain effect on deflection correction, but the current understanding of the influencing factors of deflection correction is not comprehensive. Based on structural and spatial symmetry, the influence of tunnel depth, tunnel and foundation pit clear distance and deformation control quantity of enclosure structure on deflection correction quantity was studied by symmetrically designed model test and numerical simulation, and the prediction formula of deflection correction quantity considering tunnel and foundation pit clear distance and deformation control quantity of enclosure structure was proposed. The results show that with an increase in the tunnel’s burial depth, deflection correction decreases significantly. When the tunnel is near the foundation pit bottom, there is no significant correction effect, and the control law of the tunnel ground pressure under the servo steel strut loading is consistent with the correction law. Deflection correction is negatively correlated with the tunnel and foundation pit clear distance, and positively correlated with the deformation control of the diaphragm wall. The curve of the deformation control of the enclosure structure and the deflection correction is parabolic. The deflection correction is an exponential function of the ratio of the deformation control of the enclosure structure to the clear distance between the tunnel and the foundation pit, and the servo deflection correction follows a normal distribution along the longitudinal axis of the tunnel, showing obvious symmetry characteristics in the foundation pit influence zone. Full article

The safe and efficient operation of deep-sea towing systems is heavily governed by the highly nonlinear dynamic interaction between the flexible towing cable and complex seabed topographies. While existing studies accurately predict cable dynamics in mid-water or over flat seabeds, the transient responses—such as local stress concentrations and extreme tension fluctuations—induced by discontinuous topographies (e.g., stepped or 3D irregular seabeds) remain inadequately quantified. In this study, we develop an advanced 3D dynamic numerical model combining the lumped-mass finite element formulation with a modified non-linear penalty-based seabed-contact mechanics algorithm. This framework systematically evaluates the tension distribution, bending curvature, and spatial configuration shifts in the cable during the touchdown and detachment phases across inclined, stepped, and 3D seabeds. Quantitative validation against established benchmarks demonstrates robust accuracy. Results indicate that steeper seabed inclinations linearly reduce detachment time but exponentially amplify initial contact tension. Over-stepped terrains, “point-to-line” transient collisions trigger sudden tension spikes exceeding steady-state values by up to 45%. Furthermore, 3D irregular seabeds induce severe multi-directional spatial deformations, precipitating destructive whiplash effects at high towing speeds (e.g., V > 2.2 m/s). These findings provide critical physical insights and a quantitative reference for optimizing tugboat maneuvering strategies and designing fatigue-resistant cables in complex sub-sea environments. Full article

In this work, we study a one-dimensional coupled hyperbolic–parabolic system modeling the dynamics of swelling soils under thermodiffusion effects. The model describes the interaction between the deformation of the solid skeleton, the pore fluid motion, the temperature variation, and a diffusive process formulated through chemical potential. Under mixed boundary conditions and without introducing additional mechanical damping or imposing restrictive relations among the physical parameters, we prove exponential stability of the system. Our analysis is based on the energy method. In contrast to the standard energy functional commonly used in related thermodiffusion models, we introduce a modified positive energy functional better adapted to the coupled structure of the system. By combining this energy with suitable auxiliary functionals, we construct an appropriate Lyapunov functional and derive an exponential stability estimate. Our result shows that thermodiffusion alone yields sufficient dissipation for exponential stabilization, complementing earlier works where exponential stability requires extra damping mechanisms or equal wave-speed assumptions. Full article

Fiber-optic shape sensing enables real-time monitoring of structural deformation across a wide range of applications. For large-scale structures, Brillouin-based distributed sensing, typically implemented through Brillouin Optical Time Domain Analysis (BOTDA), offers an extended range for quasi-static measurements, albeit its limited spatial resolution degrades reconstruction accuracy. This study addresses this fundamental limitation through the introduction of a novel error compensation algorithm, particularly suited for a Brillouin-based shape sensing system, yet agnostic with respect to the sensing technology. The method leverages both the initial and final points of the sensing path, performing both forward and backward reconstructions and fusing the two trajectories by testing several polynomial and exponential weighting strategies. The algorithm is experimentally validated on a 28.91 m four-core shape sensing fiber cable (length = L), interrogated through BOTDA operating at 50 cm spatial resolution, and reconstructed through the Frenet–Serret frame formulation. Calibration procedures include radial-offset tuning and segment alignment via a hotspot reference. A non-trivial S-shaped geometry is adopted as a case study, specifically addressing curvature discontinuities arising from mixed straight and curved segments. Reconstruction accuracy is quantified through a Euclidean-distance-based Figure of Merit (FOMs). The cubic weighting strategy demonstrates improvements exceeding 86% in all FOMs compared to classical methods without compensation. Specifically, it achieves an RMSE of 0.145 m (0.50% of L), a MAE of 0.109 m (0.38% of L), and a maximum error of 0.341 m (1.18% of L). Remarkably, these percentage errors are of the same order of magnitude as those reported in the literature for Fiber Bragg Grating (FBG) and Optical Frequency Domain Reflectometry (OFDR) systems, indicating that the proposed compensation strategy enables BOTDA-based shape sensing to achieve comparable reconstruction accuracy despite its lower spatial resolution. Full article

The stability of subsea tunnels is governed by the strong coupling among stress redistribution, damage evolution, and seepage flow (Stress–Damage–Seepage, SDS). The dynamic interplay, especially under high water pressure, often leads to catastrophic failures, yet its mechanisms, particularly the role of support timing, remain insufficiently understood due to limitations in conventional numerical methods. This study aims to unravel the SDS coupling mechanisms during tunnel excavation under high hydraulic head, and to quantitatively investigate how support timing influences the stability of the surrounding rock within this coupled system. A coupled Computational Fluid Dynamics and Discrete Element Method (CFD-DEM) framework was employed. In this approach, excavation-induced damage, crack propagation, and fluid–particle interactions are explicitly resolved at the particle scale, whereas the macroscopic permeability evolution is captured through an imposed empirical exponential relationship. Simulations were conducted under both steady-state and transient seepage conditions with varying stress ratios and water heads. High-head transient seepage intensifies SDS coupling, dynamically redistributing seepage forces to damage zone edges and amplifying damage. Support timing critically mediates this interaction: premature support risks tensile failure at the tunnel periphery, while delayed support allows a vicious cycle of shear failure and increased inflow. Optimal “timely” support, applied after initial deformation, diverts high seepage forces inward, minimizing final damage. The spatiotemporal synchronization of transient seepage forces with damage evolution is pivotal for stability. Support timing acts as a key control variable. The CFD-DEM framework effectively elucidates these micro-mechanisms, providing a scientific basis for the dynamic design of support in high-pressure subsea tunnels. Full article

Well spacing and reinjection rate are two critical parameters controlling the efficiency and sustainability of hot dry rock geothermal development. Taking the Yangbajing geothermal field in Tibet as the geological setting, permeability experiments were conducted on fractured rock masses under multiple operating conditions, and a three-dimensional fully coupled thermo-hydro-mechanical numerical model was established to systematically evaluate the effects of different well spacing–reinjection rate combinations on heat extraction performance. The experimental results show that axial stress is the dominant factor governing specimen deformation and seepage characteristics. Permeability decreases with increasing axial stress, exhibiting an initial sharp decline followed by a gradual reduction. The effect of temperature varies with axial stress level. Under low to moderate axial stress, permeability decreases monotonically with increasing temperature, whereas under high axial stress, it first decreases and then increases. The simulation results indicate that the production temperature remains relatively stable during the early stage of exploitation and subsequently declines, with the rate of decline increasing significantly as the reinjection rate increases or the well spacing decreases. In addition, an exponential positive relationship is identified between well spacing and the optimal reinjection rate. When a 10% decline in production temperature is adopted as the shutdown criterion, the optimal reinjection rate increases from 60 m³/h to 150 m³/h as the well spacing increases from 500 m to 800 m. Based on the simulation results, the theoretical installed capacity of the first deep reservoir in the Yangbajing geothermal field is preliminarily estimated to reach 31.8 MW. Full article

This study presents an improved methodology for assessing the environmental sensitivity of the host rock in Huashan art paintings. A hygroscopic experiment was first designed to determine the moisture diffusion coefficient of the rock mass preserving the Huashan rock paintings, as verified by hygroscopic kinetics. Additionally, variations in color difference values were simultaneously used to quantitatively evaluate moisture absorption characteristics. Subsequently, a finite element (FE) simulation was conducted to assess potential damage to the rock art system with respect to varying environmental conditions. Regarding the correlated functions with consideration of the influencing factors, the environmental sensitivity of the host rock in Huashan art paintings was clarified to illustrate the deterioration process resulting from the combined effects of temperature and humidity. It is found that the deformation gradient (F) and maximum tensile stress (σ_max) exhibit a linear relationship with ambient temperature (T_a), and an exponential relationship with heat transfer coefficient (h). The ambient humidity (H_en) and surface humidity exchange coefficient (f) primarily influence the water content of the rock mass. This insight into the host rock in Huashan art paintings provides a valuable approach to highlight the active role of environmental conditions and offers an additional methodology to understand the detachment of large superficial rock flakes and the granular disintegration of the rock. Full article

Accurate prediction of landslide displacement is crucial for hazard prevention. However, recurrent neural network (RNN) models have limitations in simultaneously capturing lag time and feature importance, and their black-box nature limits their interpretability. Moreover, the performance of single models varies across different deformation stages, especially during acceleration. To address these challenges, we propose an interpretable deep reinforcement learning-based adaptive ensemble (DRL-AE) framework. The method employs Seasonal and Trend decomposition using Loess to separate cumulative displacement into trend and periodic components. Trend and periodic sequences are predicted using double exponential smoothing and three RNN variants, respectively. An improved Convolutional Block Attention Module (ICBAM) enhances periodic feature extraction and provides temporal–spatial interpretability. The Deep Deterministic Policy Gradient algorithm adaptively integrates multi-model predictions in response to evolving environmental conditions. To validate the DRL-AE, a case study is conducted on the Baijiabao landslide in Zigui County, China. The results indicate that the DRL-AE substantially enhances prediction accuracy. For periodic displacement, it reduces MAE by 10.02% and RMSE by 6.65%, and increases R² by 4.27% compared with the ICBAM-GRU model. The results also confirm the effectiveness of ICBAM in feature extraction, and the generated heatmaps provide intuitive interpretability of the relevant triggering factors. Full article

Reinforced-soil structures in rainfall-prone regions may deform or fail when infiltration weakens the geogrid–soil interface. This study quantifies the degradation of unsaturated shear strength at a geogrid–sandy-soil interface during rainfall infiltration. A large-scale direct shear apparatus was retrofitted with a controllable rainfall system and real-time water-content monitoring. Interface shear tests were conducted under different normal stresses, rainfall intensities, infiltration durations, and shear rates. Peak interface shear strength increased approximately linearly with normal stress and remained about 50% higher than that of unreinforced sand. Rainfall infiltration caused pronounced strength loss; at 120 mm·h⁻¹, extending infiltration from 10 to 30 min reduced apparent cohesion by ~56% and friction angle by ~23%. Cohesion decayed exponentially, whereas friction angle decreased nearly linearly, and faster shearing intensified both reductions. Response-surface regression further indicates that degradation is most severe under low normal stress, high rainfall intensity, and long infiltration duration. Water-content profiles reveal a persistent moisture-enriched zone adjacent to the shear plane (~3.4% higher than at 30 mm depth), implying reduced matric suction and promoting shear-band localization that accelerates interface weakening. These findings provide quantitative input for evaluating rainfall-induced performance loss of geogrid-reinforced soil structures. Full article

Accurate prediction of post-construction settlement in high-speed railway (HSR) soft foundations is critical for operational safety yet challenging due to the non-equidistant and non-stationary nature of observation data. This study systematically evaluated the robustness and accuracy of settlement prediction models using a Monte Carlo simulation approach. A numerical model incorporating the permeability characteristics of soft foundations was established to simulate stochastic system responses. Furthermore, an innovative multi-metric evaluation framework was constructed using the entropy weight method, integrating goodness-of-fit, prediction accuracy (systematic error), and stability (random error). Four classical empirical models—Hyperbolic, Exponential Curve, Asaoka, and Hoshino—were assessed. The results indicate that: (1) The Hyperbolic Method significantly outperformed other models ($p<0.01$) in goodness-of-fit (mean correlation coefficient: 0.983 ± 0.006) and accuracy (systematic error: 3.2% ± 1.1%); (2) The Hoshino Method exhibited optimal stability, characterized by the lowest random error (3.8 ± 2.0 mm); and (3) Model performance showed a significant positive correlation with the permeability coefficient ($R^2>0.92$). Validated by five distinct engineering cases, the comprehensive performance ranking was determined as: Hyperbolic > Hoshino > Exponential Curve > Asaoka. These findings provide a scientific strategy for model selection under non-stationary conditions and offer theoretical support for refining railway deformation monitoring standards. Full article

During the high-intensity mining of shallow-buried thick coal seams, the formation of a water-conducting fracture zone within the overburden is a primary cause of damage to the groundwater system. To address the challenge of balancing efficiency and cost in traditional water-retaining mining methods, this study proposes and validates a trapezoidal strip filling mining technology based on the “span reduction effect”. By developing a mechanical model of a four-sided simply supported thin plate representing the key layer, the fundamental mechanism of the filling body was elucidated. This mechanism involves the active adjustment of the support boundary, which effectively reduces the force span of the key layer. Furthermore, leveraging the fourth-power relationship (w ∝ a⁴) between deflection and span, the bending deformation of the overburden rock is exponentially mitigated. This study employs a four-tiered integrated verification system comprising theoretical modeling, physical simulation, numerical simulation, and engineering field testing: First, theoretical calculations indicate that reducing the effective span of the key layer by 40% can decrease its maximum deflection by 87%. Second, large-scale physical similarity simulations predict that implementing this filling method can significantly control the height of the water-conducting fracture zone, reducing it from 94 m under the collapse method to 58 m, which corresponds to a 45.5% reduction in surface settlement. Third, FLAC^3D numerical simulations further elucidated the mechanical mechanism by which the backfill system transforms stress distribution from “coal pillar-dominated bearing capacity” to “synergistic bearing capacity of backfill and coal pillars”. Shear failure in the critical layer was suppressed, and the development height of the plastic zone was restricted to approximately 54 m, showing high consistency with physical simulation results. Finally, actual measurements of water injection through the inverted hole underground provide direct evidence: The heights of the water-conducting fracture zones in the filling working face and the collapse working face are 59 m and 93 m, respectively, reflecting a reduction of 36.6%. Based on the consistency between measured and simulated results, the numerical model employed in this study has been effectively validated. Research indicates that employing trapezoidal strip filling technology based on principal stress dynamics regulation can effectively promote a shift in the failure mode of the overlying critical layer from “fracture–conduction” to “bending–subsidence”. This mechanism provides a clear mechanical explanation and predictable design basis for the green mining of shallow coal seams. Full article

This paper introduces a generalized class of Weyl-type, Witt-type, and non-associative algebras constructed over an exponential–polynomial (expolynomial) framework. For fixed scalars ${\iota }_1,\dots ,{\iota }_r\in \mathcal{A}$ and for fixed integers $\mathbf{p}=(p_1,\dots ,p_n)\in {\mathbb{N}}^n$, we define the $\mathbb{F}$-algebra $\mathbb{F}\left[e^{\pm x^{\mathbf{p}}{e}^{\iota x}},e^{\mathcal{A}x},x^{\mathcal{A}}\right],$ an expolynomial ring over a field $\mathbb{F}$ of characteristic zero, where $\mathcal{A}$ is an additive subgroup of $\mathbb{F}$ containing $\mathbb{Z}$. This formulation extends the classical Weyl algebra through the integer power parameter $\mathbf{p}$, which generates a family of non-isomorphic simple algebras. The corresponding Weyl-type algebra $A\left(\mathbb{F}[e^{\pm x^{\mathbf{p}}{e}^{\iota x}},e^{\mathcal{A}x},x^{\mathcal{A}}]\right),$ the Witt-type Lie algebra $W\left(\mathbb{F}[e^{\pm x^{\mathbf{p}}{e}^{\iota x}},e^{\mathcal{A}x},x^{\mathcal{A}}]\right),$ and their non-associative variants are examined in detail. The simplicity, grading, and automorphism structures of these algebras are established, and the dependence of these properties on the deformation parameter $\mathbf{p}$ is analyzed. All the constructed Weyl-type algebras, the corresponding Witt-type Lie algebras, and the non-associative algebras are shown to be simple under derivation structures. Many naturally occurring subalgebras, such as the integer-coefficient subalgebra $A\left(\mathbb{Z}[e^{\pm x^{\mathbf{p}}{e}^{\iota x}},e^{\mathcal{A}x},x^{\mathcal{A}}]\right)$, are also proven to be simple. Our analysis reveals that different choices of $\mathbf{p}$ result in non-isomorphic algebraic structures while retaining non-commutativity. The results obtained generalize several existing constructions of Weyl-type algebras and lay the theoretical foundation for further developments in transcendental and non-commutative algebraic frameworks. Full article

Supercritical CO₂ modifies deep coal reservoirs through the coupled effects of adsorption-induced deformation and geochemical dissolution. CO₂ adsorption causes coal matrix swelling and facilitates micro-fracture propagation, while CO₂–water reactions generate weakly acidic fluids that dissolve minerals such as calcite and kaolinite. These synergistic processes remove pore fillings, enlarge flow channels, and generate new dissolution pores, thereby increasing the total pore volume while making the pore–fracture network more heterogeneous and structurally complex. Such reservoir restructuring provides the intrinsic basis for CO₂ injectivity and subsequent CH₄ displacement. Both adsorption capacity and volumetric strain exhibit Langmuir-type growth characteristics, and permeability evolution follows a three-stage pattern—rapid decline, slow attenuation, and gradual rebound. A negative exponential relationship between permeability and volumetric strain reveals the competing roles of adsorption swelling, mineral dissolution, and stress redistribution. Swelling dominates early permeability reduction at low pressures, whereas fracture reactivation and dissolution progressively alleviate flow blockage at higher pressures, enabling partial permeability recovery. Injection pressure is identified as the key parameter governing CO₂ migration, permeability evolution, sweep efficiency, and the CO₂-ECBM enhancement effect. Higher pressures accelerate CO₂ adsorption, diffusion, and sweep expansion, strengthening competitive adsorption and improving methane recovery and CO₂ storage. However, excessively high pressures enlarge the permeability-reduction zone and may induce formation instability, while insufficient pressures restrict the effective sweep volume. An optimal injection-pressure window is therefore essential to balance injectivity, sweep performance, and long-term storage integrity. Importantly, the enhanced methane production and permanent CO₂ storage achieved in this study contribute directly to greenhouse gas reduction and improved sustainability of subsurface energy systems. The multi-field coupling insights also support the development of low-carbon, environmentally responsible CO₂-ECBM strategies aligned with global sustainable energy and climate-mitigation goals. The integrated experimental–numerical framework provides quantitative insight into the coupled adsorption–deformation–flow–geochemistry processes in deep coal seams. These findings form a scientific basis for designing safe and efficient CO₂-ECBM injection strategies and support future demonstration projects in heterogeneous deep coal reservoirs. Full article

The accurate prediction of the behaviour of piles is a particularly important stage of structural design. The dependence of pile settlement and load is often very important for soil–structure interaction in the design of structures. The distribution of stresses and deformations to the structures above also depends partly on the pile settlement. Therefore, the correct assessment of this stage is important in order to have the correct parameters of the building calculation scheme. Before starting the design of building foundation structures and above-ground structures, geological surveys are carried out. When designing according to Eurocodes, a certain number of field tests must be carried out to verify the design assumptions. The pile static load tests provide load and settlement curves. There are several most common ways to describe these curves in mathematical expressions. And the more these expressions correspond to the results of real tests, the more accurately the behaviour of pile foundations can be described. Based on the real results of pile tests, an analysis of methods for describing pile behaviour is performed. The article presents the most popular methods used to describe load–settlement: quadratic hyperbolics, power law, exponential and rectangular hyperbolics. A statistical analysis of the accuracy of the methods is presented. The accuracy of the four methods studied was determined based on the statistical analysis, and their reliability was discussed. The most suitable dependence for practical design was then proposed. Full article