To better characterize the intricate coupled thermo-hydro-mechanical dynamic (THMD) response in twodimensional saturated soil and to enrich the research object of Green-Naghdi (G-N) generalized thermoelastic theory, this study innovatively combines the G-N generalized thermoelastic theory and Caputo's fractional order derivative, to obtain the new control equations, and to establish a new fractional order thermoelastic theoretical model. The article is solved by the normal mode analysis (NMA), which can eliminate the integration error and solve the complex fractional order partial differential control equations quickly at the same time. The effects of different boundary conditions of fractional order derivatives, porosity, frequency, and thermal conductivity coefficients on non-dimensional excess pore water pressure, temperature, vertical displacement, and vertical stress are also fully analyzed, and the distribution curves of high precision numerical solutions are given. The results show that the effect of frequency variation on each non-dimensional variable is obvious. The effects of fractional order derivatives, porosity and thermal conductivity coefficients on the non-dimensional variables vary depending on the boundary conditions. The results provide theoretical support for geotechnical and environmental engineering.

Fractional calculus is a powerful mathematical tool for solving mechanical modeling problems. It is used to simulate soils between ideal solids and fluids. Using Riemann-Liouville's fractional calculus operator and theory, fractional order viscous element, nonlinear viscous element and viscoplastic body are connected in series to establish a fractional nonlinear creep damage model, which is used to simulate the nonlinear gradient process of rock creep under different water content conditions. The constitutive equation of the model is constructed. The parameters of creep damage model are identified based on the principle of least squares. The results show that the correlation between theoretical model and experimental data is more than 0.98, which can simulate the creep characteristics of rock well. The effect of model parameters on deformation is further explored, so that the effectiveness of model parameters can be analyzed and verified, and the applicability of the model in other complex stress environments is increased. The research results can provide theoretical basis for stability analysis and disaster prevention of soft rock slopes.

BackgroundThe dynamic coupled hydro-thermo-mechanical behavior of the unlined structure in saturated porous structure under extreme geotechnical and geology engineering (e.g., underground explosion, laser thermal rock breaking) have aroused extensive research interests on the constitutive modeling and transient dynamic responses prediction. Although the current fractional-order hydro-thermo-mechanical models have been historically proposed, the theoretical formulations still adopt the classical fractional derivatives with singular kernels, and the inherent strain relaxation effect and the associated memory dependency remains not considered yet in such complex condition.PurposeTo compensate for such deficiencies, the current work aims to establish the new hydro-thermo-mechanical model by introducing the Atangana-Baleanu (AB) and Tempered-Caputo (TC) fractional derivatives with non-singular kernels.MethodsThe proposed model is applied to investigate transient structural dynamic hydro-thermo-mechanical response of a cylindrical unlined tunnel in poroelastic medium by applying Laplace transformation approach.ResultsThe influences of the AB and TC fractional derivatives on the wave propagations as well as the dimensionless responses of the temperature, displacement, stress, and pore-water pressure are evaluated and discussed.ConclusionThe non-singular AB and TC fractional derivatives slower the thermal wave propagation. In addition, the dimensionless pore water pressure dissipation is maximally reduced. The increase of strain relaxation time parameter reduces the mechanical dynamic response regions and eliminates the sharp jumps of mechanical response at the elastic wave front, which are consistent with continuity of displacement in real engineering situations.

The strain paths of cement stone in the deviatoric and meridian planes under the constant Lode angle loading path (true triaxial stress state) are analyzed. The amount of volumetric and shear strains first increases and then decreases with the intermediate principal stress coefficient. Owing to the generation of plastic volumetric strain and plastic shear strain in the direction of deviatoric stress, the strain path exhibits nonlinearity in the meridian planes. The deviation of the strain path from the constant Lode angle arises from the accumulation of plastic shear strain along the Lode angle direction. In the framework of fractional plasticity, a three-dimensional elastoplastic constitutive model incorporating Lode angle is proposed, including yield function, potential function, and fractional flow rule. The yield surface evolves in both meridian and deviatoric planes, allowing the yield function to precisely characterize the stress state. Since the plus-minus sign in the flow direction of the yield surface is opposite to that in the flow direction of cement stone, a simple elliptic function incorporating Lode angle serves as the potential function. The procedure for the determination of fractional order based on the entirety of the deformation process is proposed, including variable and constant fractional order. The comparison between the experimental result and the analytical solution of constitutive model confirms its accuracy and validity. Furthermore, the difference between variable and constant fractional order on deformation is analyzed. The comparison results indicate that the variable fractional order can provide a more accurate description of deformation than the constant fractional order.

Laminar flow phenomena may occur when pore water flows at low velocities across the interfaces between soils of different properties, thus causing flow contact resistance. To explore the impacts of interfacial flow contact resistance and rheological characteristics on the thermal consolidation process of layered viscoelastic saturated soil foundation featuring semi-permeable boundaries. This paper established a new thermal consolidation model by introducing a fractional order derivative model, Hagen-Poiseuille law and time-dependent loadings. The semi-analytical solutions for the proposed thermal consolidation model are derived through the Laplace transform and its inverse transform. The reliability and correctness of the solutions are verified with the experimental data in literatures. The influence of constitutive parameters, flow contact resistance model parameters on thermal consolidation process and the interfacial flow contact resistance on foundation settlement, is further explored. The results indicate that the impact of the constitutive parameters and permeability coefficient on the thermal consolidation of viscoelastic saturated soil is related to the flow contact resistance. The enhanced flow contact resistance effect leads to a significant increase in pore water pressure and displacement during the consolidation process.

The Dunhuang murals are a precious treasure of China's cultural heritage, yet they have long been affected by salt damage. Traditional methods for detecting salt content are costly, inefficient, and may cause physical harm to the murals. Among current techniques for measuring salt content in murals, hyperspectral remote sensing technology offers a non-invasive, circumventing issues of high costs, low efficiency. Building on this, the study constructs an inversion model for the Electrical Conductivity (EC) values of mural plaster subjected to phosphate erosion, through the integration of Fractional Order Differentiation (FOD), a novel three-band spectral index, and the Partial Least Squares Regression algorithm. The specific research contents include: (1) Initially, in preparation for the experiments, the materials used to create the samples underwent a rigorous desalting process, and phosphate solutions were prepared using deionized water to ensure uniform experimental conditions and the accuracy of the results. These meticulous preprocessing steps guaranteed that the measured EC values exhibited a clear correlation with the phosphate content. Subsequently, by employing qualitative experimental analysis techniques, this study was able to more accurately simulate the real-world scenarios of mural plaster affected by salt damage, enabling a deeper investigation into the mechanisms by which salts inflict microscopic damage to murals. (2) Explores the absorption mechanisms and characteristic spectral bands of the Electrical Conductivity (EC) values measured after the phosphate erosion of mural plaster. By integrating the optimal spectral indices, a univariate linear regression model is constructed, providing a basis for the rapid quantitative measurement of electrical conductivity in murals. (3) By comparing the accuracy of the Phosphate Simple Ratio (PSR) and Phosphate Normalized Difference Index (PNDI) spectral indices based on the linear regression model, the first six orders of the highest accuracy spectral index were selected as the optimal three-band spectral index combination, used as explanatory variables, with mural plaster electrical conductivity as the response variable, employing the PLSR method to construct the mural phosphate content high-spectral feature inversion model. The study's findings include: (1) Surfaces of samples deteriorated by phosphate erosion formed numerous irregularly shaped crystal clusters, exhibiting uneven characteristics. (2) By comparing the outcomes of different orders of fractional differentiation, it was found that the model performance reached its optimum at a 0.3 order of differentiation for both PSR and PNDI data, with a determination coefficient (Q2) of 0.728. (3) Utilizing PLSR, this study employed the previously determined optimal six-order three-band spectral index combination as explanatory variables, with salt content as the response variable, successfully constructing the high-spectral feature inversion model for mural electrical conductivity with a determination coefficient (Q2) of 0.815. This provides an effective technical means for monitoring the salt damage conditions of precious cultural heritage such as murals.

Based on Biot porous medium theory, considering the coupled reaction of soil skeleton rheology and pore pressure dissipation, the present work investigates the dynamic consolidation characteristics of saturated clay ground under cyclic loading. First, the rheological behavior of the soil skeleton was described by the fractional order Kelvin model. The dynamic consolidation governing equations for the saturated clay were established theoretically in a three-dimensional axisymmetric coordinate system. Second, the transform domain analytical solution of the dynamic consolidation of saturated clay was obtained using the Hankel-Laplace coupled transform method, and the solution in the time-space domain was further obtained through numerical inversion. Finally, the rheological consolidation behavior of saturated clay under cyclic loading and the influences of parameters were analyzed. The results show that the rheology of the soil skeleton had an inhibitory effect on pore water permeability; compared with elastic skeleton soil, the rheological clay had a slower settlement rate in the primary consolidation stage, a faster rate in the secondary consolidation stage, and greater long-term settlement. In addition, under cyclic loading, the pore pressure response in saturated clay lags behind the effective stress, and a larger viscous order is associated with faster development of cumulative settlement.

The soft interlayer, often considered the weak link of slopes, poses a significant threat to slope stability. This study focuses on the Permian carbonaceous shale soft interlayer commonly found in Southwest China. The creep characteristics of the soft interlayer were investigated, and a graded shear creep test was conducted in addition to conventional shear tests to analyze the shear deformation behavior of the soft interlayer comprehensively. The long-term strength of the soft interlayer was determined using the steady-state creep rate method. Building upon the Riemann-Liouville fractional order integral theory and statistical damage theory, an improved model based on the traditional Nishihara model was developed. The accuracy of the model was verified using the adaptive differential evolution algorithm in combination with the weak interlayer shear creep test curve, followed by a parameter sensitivity analysis. The results demonstrate that the improved model adequately describes the three stages of creep in the weak interlayer. The creep curve is influenced by the differential order., the shape parameter m, and the proportional parameter F-0. Parameter m reflects the brittle characteristics of the soft interlayer, while parameter F-0 characterizes its physical and mechanical strength. The research results can provide a theoretical basis for disaster prevention monitoring and stability analysis of slopes with weak interlayer.

The Dunhuang murals are a precious treasure of China's cultural heritage, yet they have long been affected by salt damage. Traditional methods for detecting salt content are costly, inefficient, and may cause physical harm to the murals. Among current techniques for measuring salt content in murals, hyperspectral remote sensing technology offers a non-invasive, circumventing issues of high costs, low efficiency. Building on this, our study developed a high-spectral feature inversion model for mural phosphate content using Fractional Order Differentiation (FOD), a novel three-band spectral index, and Partial Least Squares Regression (PLSR) algorithm. The specific research contents include: 1) Exploring the absorption mechanism of phosphates and their characteristic bands, combined with the optimal spectral index to construct a univariate linear regression model, providing a basis for rapid quantitative measurement of mural phosphate content. 2) By comparing the accuracy of the PSR and PNDI spectral indices based on the linear regression model, the first six orders of the highest accuracy spectral index were selected as the optimal three-band spectral index combination, used as explanatory variables, with mural plaster electrical conductivity as the response variable, employing the PLSR method to construct the mural phosphate content high-spectral feature inversion model. The study's findings include:1) By comparing the outcomes of different orders of fractional differentiation, it was found that the model performance reached its optimum at a 0.3 order of differentiation for both PSR and PNDI data, with a determination coefficient (R-2) of 0.728. 2) Utilizing PLSR, this study employed the previously determined optimal six-order three-band spectral index combination as explanatory variables, with salt content as the response variable, successfully constructing the high-spectral feature inversion model for mural phosphate content with a determination coefficient (R-2) of 0.815. This provides an effective technical means for monitoring the salt damage conditions of precious cultural heritage such as murals.