Viscoelastic materials differ fundamentally in their retardation spectrum characteristics. Conventional fractional-order models cannot accommodate such spectral diversity within a unified framework. To address this, a generalized ψ -Caputo fractional-order Burgers ( ψ -CFB) model is developed in this work, which enables flexible kernel function selection according to material characteristics. A spectral width factor Λ (t) is introduced to establish a mathematically grounded kernel function selection criterion. The power-law kernel is suggested for broad-spectrum materials, the exponential kernel for narrow-spectrum materials, and the logarithmic kernel for materials with intermediate spectral width. The Kachanov damage theory and the Schapery nonlinear viscoelastic theory are incorporated according to the specific characteristics of the target materials. Three representative viscoelastic materials with distinct retardation spectrum features, namely asphalt, polylactic acid (PLA), and polycarbonate (PC), are selected for assessment. The results under unconstrained single-stress fitting show that the ψ -CFB model provides accurate fitting for asphalt under high-stress conditions (Adj-R2 = 0.9995, MAPE = 0.598 ψ -CFB parameters with a few stress or data-scale factors, and the results confirm that the proposed model also agrees with the experimental data under this joint-fitting scheme.
The deep rock mass has long been subjected to a complex geomechanical environment of “three highs and one disturbance,” rendering the structural characteristics and mechanical behavior of deep rock masses more complex. The −850 m roadway in Qujiang Coal Mine is longitudinally tiled under the 805 working face and coal pillar. Affected by the mining of the upper working face and the bias of the coal pillar, the roadway presents various deformation and damage characteristics. The deformation and damage patterns of the dynamic pressure roadway of the back mining are analysed through field investigation, bolt and anchor cable force monitoring, and peripheral rock deformation monitoring, and the proposed support countermeasures are verified and analysed by using FLAC3D numerical software. The results show that: (1) Using bolt/anchor cable axial force monitoring and surrounding rock deformation monitoring, it is found that the mining-induced dynamic pressure −850 m roadway displays distinct zonal damage characteristics, which can be divided into a rear sustained (high-pressure) deformation zone and a forward disturbance (dynamic-pressure) deformation zone. (2) In the forward disturbance (dynamic-pressure) deformation zone, damage mainly occurs in the upper roof of the roadway, predominantly as sliding shear damage; in the rear sustained (high-pressure) deformation zone, damage mainly occurs at the floor and the arch foot. The floor is prone to plastic extrusion deformation and damage, while the arch foot mainly experiences punching shear and internal folding damage. (3) According to the different damage modes of the −850 m roadway, it is proposed to implement “three-anchor” combined support technology in the rear sustained (high-pressure) deformation zone, and to implement “resistance-yielding combined” support in the forward disturbance (dynamic-pressure) deformation zone. (4) FLAC3D numerical simulation results are consistent with the field monitoring data, confirming the rationality and effectiveness of the proposed zonal support measures. The research results provide a certain reference for surrounding rock deformation control in deep mining dynamic pressure roadways in the future.
The accelerated creep behaviour of rock under varying confining pressures is critical to the long-term stability of rock engineering structures, yet its nonlinear evolution remains difficult to characterize. In this study, triaxial creep tests with coupled confining pressure and pore-water pressure are performed, and the evolution of the viscoplastic strain rate is investigated together with published experimental data. A nonlinear increase in the normalized strain rate with viscoplastic deformation is identified, with a pronounced dependence on confining pressure. On the basis of parameter sensitivity analyses, the viscosity coefficient is identified as the primary parameter governing accelerated creep evolution within the framework of overstress theory. Inspired by the reported correspondence between accelerated creep and the post-peak stage, an internal variable κ is introduced to characterize the coupled effects of viscoplastic strain accumulation and confining pressure on accelerated creep evolution. On this basis, an exponential evolution law for viscosity is established, laying the foundation for an improved viscosity-evolution-based Nishihara model. The proposed model can accurately reproduce the key characteristics of rock creep processes and effectively capture the influence of confining conditions on accelerated behaviour. Furthermore, applications to several rock types reported in the literature demonstrate the applicability of the proposed constitutive model to different rock materials after parameter calibration.
To investigate the mechanical response and damage evolution of surrounding rock subjected to repeated dynamic disturbances in deep underground engineering, cyclic impact tests on granite were conducted using a split Hopkinson pressure bar (SHPB) system under different incremental gas-pressure gradients, with constant-amplitude repeated impact tests performed for comparison. The results indicate that, under constant-amplitude repeated impact loading, the dynamic strength and dynamic elastic modulus generally decrease with increasing impact number, demonstrating a degradation process dominated by damage accumulation. Under incremental cyclic impact loading, the dynamic strength increases markedly with increasing impact amplitude; however, crack propagation during the later loading stage leads to stiffness degradation and sudden failure, reflecting competition among strain-rate strengthening, cyclic compaction, and damage-induced degradation. Energy analysis shows that the cumulative dissipated energy increases continuously with impact number. Under incremental cyclic impact loading, a larger impact-amplitude increment accelerates damage accumulation and causes the specimen to enter the high-damage regime at an earlier stage. The energy-based damage variable D effectively characterizes the damage evolution process and exhibits good agreement with the observed macroscopic failure characteristics. The results demonstrate that the impact-amplitude increment governs the rate and critical process by which granite transitions from compaction-induced strengthening to damage-dominated instability, while the stability of surrounding rock primarily depends on whether internal damage approaches the critical state of crack coalescence. These findings provide a theoretical basis for stability assessment of deep surrounding rock and the control of blasting-induced disturbances.
The creep response of composite salt rock depends on mineral composition, however, quantitative constitutive models that account for composition effects remain limited. In this paper, composition-controlled synthetic salt rock cores were prepared by high-temperature axial compaction using halite as the matrix and anhydrite or sylvite as accessory minerals. Anhydrite-halite specimens contained 0-80 wt.
Deep coal rocks exhibit complex nonlinear rheological properties under high-stress environments, so conventional integer-order creep models cannot describe the full creep process, especially the accelerated phase. This paper introduces a novel variable-order fractal dashpot into the constitutive modeling of coal rocks. The fractal derivative is a strictly local operator that avoids the convolutional integration required by fractional derivatives, offering closed-form analytical solutions, the ability to accommodate variable-order and damage-coupled parameters without inflating computation, and concise expressions free of special functions. Defining the fractal order as a function of time and cleat-damage evolution lets the dashpot capture the progressive deterioration of the rock’s mechanical properties. Replacing the Newtonian dashpot in the classical Maxwell model with this element yields a new nonlinear creep damage model. An intelligent parameter-identification method based on Adaptive Particle Swarm Optimization (APSO) is proposed for the hard-to-invert nonlinear equation. Analytical solutions are derived and validated against cited triaxial creep data of coal rocks. The APSO-based fitting shows that the model reproduces the primary, steady-state, and highly nonlinear tertiary creep stages with physically reasonable parameters ( R^2=0.9984 ), outperforming the integer-order Nishihara model and a constant-order fractional model. A quantitative comparison further shows that the local fractal operator is roughly two orders of magnitude faster than the global fractional operator, with the gap widening as the number of evaluation points increases. The scope and limitations are discussed explicitly.
Weakly cemented soft rock exhibits strong water sensitivity and time-dependent deformation, which can threaten the long-term stability of foundations and underground structures. In this paper, triaxial creep tests were conducted on weakly cemented soft rock specimens with moisture contents of 0
Constitutive models currently implemented in numerical simulation tools had limited applicability and cannot accurately characterize the complex creep behavior of magnetite. Here, we derive a three-dimensional central-difference formulation from the one-dimensional constitutive equation of the nonstationary viscoelastic-plastic BuCY creep model, based on rock rheology theory. We further enhance the numerical solution framework to perform iterative stress-strain updates within each time step. During the accelerating creep stage of the nonstationary viscoplastic CY component, the plastic behaviour of element Y is governed by the Mohr-Coulomb instability criterion. The BuCY creep model able to reproduce the observed creep characteristics of the magnetite-was integrated into the finite-difference code via secondary development, enabling model compilation and solution algorithm and inverse verification. Numerical simulation and inversion results show close agreement, confirming the success of the implementation. Comparative analysis with conventional creep models further confirms the superior applicability and accuracy of the BuCY model. This research significantly improves the fidelity of numerical simulations and is particularly well suitable for practical engineering problems, such as the analysis of deeply buried mining stopes.
Reliable prediction of grout migration and sealing performance remains critically challenging since natural fracture network is geometrically complex and inherently opaque to direct observation. Existing predictive approaches for grouting design and performance assessment often simplify grout-water interactions via single-phase flow idealizations, and the time-dependent evolution of grout rheology is inadequately represented, particularly for realistic three-dimensional fracture systems. In this study, we develop a new computational model for immiscible two-phase grout-water flow based on the fractured porous media framework. By further incorporating hydration-induced viscosity evolution and reconstructing three-dimensional discrete fracture network, the spatial transport of hydrating grout in stochastically fractured rock mass has been rationally captured. The numerical results reveal that the spatial topology and connectivity characteristics of discontinuity systems dictate preferential grout penetration pathways, yielding strongly anisotropic and path-dependent diffusion patterns. Meanwhile, the progressive pressure attenuation and viscosity growth can contribute to pronounced deceleration of grout diffusion. Application to high-pressure grouting at a pumped storage hydropower project demonstrates that, increasing the injection pressure from 2 MPa to 8 MPa raises the fracture sealing ratio from 11.92
The creep behavior of water-bearing sandy mudstone is important for evaluating the long-term stability of underground engineering structures. In this paper, triaxial compression and triaxial creep tests were conducted on natural and dry sandy mudstone to examine the effects of water, deviatoric stress, and confining pressure on strength and creep deformation. The results show that water significantly weakens sandy mudstone, reducing its compressive strength, tangent modulus, cohesion, and long-term strength while increasing creep strain and steady-state creep rate. Increasing confining pressure improves the deformation resistance and long-term load-bearing capacity of the rock. Based on the experimental results, an extended Burgers nonlinear creep model was developed by incorporating water-induced damage, viscoplastic deformation, and a nonlinear viscosity coefficient for the accelerated creep stage. The proposed model reproduces the triaxial creep curves well, with coefficients of determination R^2≥ 0.967 . The model was implemented in numerical simulations through secondary development and validated against the laboratory creep tests, with a maximum error of 13.85
Creep behavior plays an important role in the long-term reliability of composite structures, but its nonlinear and time-dependent nature makes accurate prediction difficult. In this study, a combined experimental-theoretical-numerical approach is proposed to characterize the nonlinear creep behavior of fiber-reinforced composites under different stress levels. First, a three-dimensional constitutive model is proposed based on the generalized Hill yield criterion and the Perzyna overstress function to describe multiaxial viscoplastic flow with tension-compression asymmetry. The model further incorporates the strain-rate dependence of the yield stress through the Eyring function, which improves the description of the initial rapid creep response. Then, the model is implemented into ABAQUS software through a user-defined subroutine using an algorithmic tangent operator and a return-mapping-type stress update algorithm. Finally, the proposed model is validated against compression creep experiments over a stress range from 20 to 80 MPa, and its predictive performance is systematically compared with those of the time-dependent consititutive models, showing consistently better agreement with the experimental results. The proposed approach provides a practical tool for long-term creep prediction and reliability assessment of composite structures.
Fault-crossing roadways often experience severe stress perturbation and large deformation, posing critical challenges to surrounding rock control. Taking the Duanwang Coal Mine as a case study, this study investigates the evolutionary characteristics of the plastic zone and stress redistribution mechanisms induced by fault structures. The results show that the presence of a fault substantially alters the in-situ stress field, producing a pronounced stress concentration near the fault interface. An increased lateral pressure coefficient promoted the extension of plastic zones in both the roof and floor, whereas reductions in the Geological Strength Index and uniaxial compressive strength accelerated the nonlinear expansion of plastic failure. Numerical simulations further revealed that the fault dip angle plays a decisive role in stress distribution: low-angle faults induce greater stress asymmetry and result in more significant shear deformation on the roof–floor system. Based on the spatial pattern of rock deformation, a zonal support strategy was proposed. Within the fault-influenced zone, a composite support system consisting of bolts, cables, and a steel-frame canopy was adopted, while a full-length anchorage scheme was applied in high-stress concentration areas. Field monitoring indicated that the optimized support system effectively restrained roof subsidence and rib convergence, with bolt and cable load levels stabilizing within safe bearing limits. The deformation rate of the surrounding rock was significantly reduced. This study provides a theoretical foundation and practical guidance for the design and optimization of support systems in fault-affected roadways.
Controlling blast-induced damage is important for underground construction in island and reef engineering. This paper investigates the transient strain response and damage evolution of reef limestone under radially decoupled charging through laboratory model blasting experiments and three-dimensional numerical simulations. Cylindrical reef limestone specimens with radial decoupling coefficients K_d of 1.0, 1.25, 2.0, and 2.5 were tested. Strain gauges were used to record blast-induced strain histories, while post-blast crack patterns were analyzed using image processing and box-counting fractal analysis. The results show that K_d has a significant non-monotonic effect on peak tensile strain, crack development, and fractal dimension. The peak tensile strain increased from 2.09 ε at K_d = 1.0 to a maximum of 2.28 ε at K_d = 1.25 , then decreased to 1.13 and 0.99 ε at K_d = 2.0 and 2.5, respectively. The crack network also reached its highest fractal dimension of 1.5799 at K_d = 1.25 , indicating the most developed multiscale cracking pattern. Numerical simulations further show that increasing K_d attenuates stress-wave amplitude, modifies wave propagation, and promotes a transition from extensive crack development to more localized damage near the blasthole. These findings suggest that an intermediate radial decoupling coefficient, particularly K_d = 1.25 , can provide a favorable balance between blasting efficiency and damage control in porous reef limestone. The results provide guidance for precision blasting design and damage mitigation in reef-island underground engineering.
Modeling viscoelastic vibration remains a persistent challenge due to memory effects, coupled dynamics, and the difficulty of linking data-driven models with physical interpretability. Conventional approaches, such as Prony-series identification or fractional calculus formulations, capture relaxation behavior but rely on handcrafted parameterization and are sensitive to numerical discretization. To address these limitations, we propose a physics-informed neural framework that integrates a causal temporal convolutional encoder with a Neural Prony State-Space Layer (NPSSL), a differentiable realization of the linear Volterra operator that generalizes the classical Prony model—and three supervised heads for multi-step displacement forecasting, kernel-family classification, and Prony-amplitude regression. The NPSSL explicitly parameterizes relaxation dynamics as a discrete-time hereditary memory with nonnegative amplitudes, while a physics residual term enforces consistency with the governing second-order oscillator equation balancing forcing, inertia, stiffness, and viscoelastic stress. The proposed framework is first evaluated on synthetic benchmarks covering single-Maxwell, multi-exponential Prony, stretched-exponential, and power-law kernels, where it achieves near-perfect kernel classification, sub-percent forecasting error, and accurate recovery of relaxation spectra. Normalized physics residuals remain approximately unbiased on synthetic data with unit-scale dispersion, confirming stable physical alignment across solvers. To further evaluate generalization in real-world scenarios, the model is validated using the experimental Linear Particle Chain Impact Damper dataset. The NPSSL accurately replicates the observed displacement dynamics, achieving a R^2≈ 0.73 and exhibiting well-behaved residuals. This illustrates that integrating a differentiable Volterra-type memory into a neural architecture facilitates both interpretability and precision, connecting classical hereditary mechanics with real-world dissipative vibration phenomena.
The growing emphasis on low-carbon and sustainable mining has intensified interest in alternative cementitious materials for cemented tailings backfill (CTB). However, the dynamic mechanical behavior of CTB incorporating fully solid-waste cementitious material remains insufficiently characterized. In this study, a fully solid-waste cementitious material composed of ground granulated blast-furnace slag, desulfurization gypsum, and fly ash was developed and applied to CTB. Using the glue-bone ratio, mass concentration, and average strain rate as variables, the dynamic compression tests were performed with a split Hopkinson pressure bar system to investigate the impact response of fully solid-waste cemented tailings backfill (FSWCTB). The strain-rate-dependent stress-strain behavior curves, dynamic compressive strength and failure morphology were analyzed, and the applicability of the Z-W-T constitutive model to FSWCTB was further evaluated. Furthermore, nuclear magnetic resonance and scanning electron microscopy coupled with energy dispersive spectroscopy were used to elucidate the microstructural features and hydration mechanisms of the FSWCTB material. Results indicated that (1) the dynamic compressive strength of FSWCTB increased progressively with higher glue-bone ratio, mass concentration, and average strain rate. (2) when the average strain rate increased to 415 s−1, the failure mode of the FSWCTB specimens transitioned from localized collapse to global fragmentation. (3) The increase in glue-bone ratio and mass concentration led to the formation of a denser microstructure, which was beneficial for the development of backfill strength. The findings provide fundamental insights into the dynamic performance of FSWCTB and support its sustainable application in underground mining engineering.
The construction industry faces increasing environmental challenges due to the overexploitation of natural sand and the growing volume of construction and demolition (C D) waste. Utilizing recycled sand (RS) derived from C D waste offers a sustainable alternative, contributing to resource conservation and circular economy practices. This study examines the feasibility of using RS as a substitute for natural sand (NS) in cement mortar, with a focus on thermal stability at elevated temperatures. Five mortar mixes were prepared by substituting NS with RS at 0
This study investigates the rotational flow behavior and thermal transport characteristics of a chemically reactive viscous fluid subjected to a uniform magnetic field, with potential applications in advanced energy and thermal management systems. A fractional modeling framework based on the constant proportional Caputo derivative is employed to capture nonlocal and memory-dependent diffusion effects in the transport processes. The fluid flows over an infinite vertical plate undergoing arbitrary motion with Newtonian heating conditions, while the ambient temperature and concentration are maintained at T_∞ and C_∞ , respectively. Through suitable similarity transformations, the governing momentum, energy, and concentration equations are converted into a dimensionless form and solved analytically to obtain closed-form expressions for the velocity, temperature, and concentration fields. The influence of key dimensionless parameters is examined in detail. The results indicate that an increase in the fractional order parameter enhances the momentum and thermal boundary layers, producing approximately 15– 25% enhancement in the velocity distribution, 10– 20% increase in the temperature field, and about 12– 18% growth in the concentration profile near the plate. Furthermore, the magnetic interaction parameter suppresses the velocity field due to the presence of the Lorentz force, whereas the chemical reaction parameter significantly modifies the concentration boundary layer thickness. These results highlight the effectiveness of fractional calculus in accurately describing memory-dependent transport phenomena and demonstrate the important role of governing dimensionless parameters in optimizing the performance of modern thermal systems.
In this study, the free vibration behavior of perforated viscoelastic nonlocal Timoshenko beams has been investigated using a semi analytic method based on the Fourier series and the Stokes transformation. First, the geometric structure of the perforated beam was defined; then, by combining the Kelvin–Voigt viscoelastic model with the theory of nonlocal elasticity, the equations of motion describing the system were derived. During the solution phase, the boundary conditions of the beam were reduced to an eigenvalue problem using a semi analytic approach, with spring elements restricting rotation at both ends, and high-accuracy results have been obtained under various boundary conditions. The findings indicate that an increase in the nonlocal scale parameter has a softening effect on structural stiffness, thereby reducing vibration characteristics. Additionally, it is observed that an increase in the number of holes enhances discontinuity along the beam, leading to significant changes in system behavior. It is determined that the viscoelastic damping effect becomes more dominant, particularly under rigid boundary conditions, but weakens as the perforation density increases. The study also reveals that the void ratio, shear deformation, and boundary conditions are in strong interaction with one another. The proposed method offers an effective and reliable methodological approach for the dynamic analysis of perforated nanostructures, thanks to both its high convergence performance and its ability to model different boundary conditions within the same formulation.
In southwestern China, limestone is the primary raw material for cement production, and its extraction and processing generate large amounts of limestone powder waste. This powder is commonly used in high embankments and slope engineering projects. A clear understanding of its long-term deformation behavior under self-weight loading is therefore essential for evaluating slope stability. In this study, the creep behavior of limestone powder is investigated using a series of triaxial consolidated undrained creep tests conducted under different confining pressures. This study proposes a novel fractal viscoelastic accelerated creep model (F-VEAP model). The model extends the linear Newtonian viscoelastic formulation to a nonlinear fractal Newtonian viscoelastic framework by introducing a fractal derivative, β , thereby capturing nonlinear steady-state creep behavior. An exponentially accelerated term derived from damage mechanics is incorporated to represent the accelerated creep stage. Based on model parameter identification, the F-VEAP model is shown to effectively capture the full-stage creep behavior of limestone powder. Results of the parameter sensitivity analysis further indicate that individual model parameters distinctly influence creep behavior and can serve as a useful basis for distinguishing different creep stages. Comparative analyses with the classical Burgers model and the fractional-order derivative-based FFC model demonstrate that the proposed model provides an improved representation of the observed creep behaviour. The proposed framework offers a useful basis for analysing the long-term deformation characteristics of limestone powder and similar fill materials in slope engineering and may provide reference for the deformation assessment of cement-based fill materials; however, its broader applicability still requires further validation.
