Previous theoretical studies on the deformation of shield tunnels induced by foundation pit excavation generally consider the stratum as a linear elastic body, which seldom take the irregular construction boundary into account. Meanwhile, Curved beam theory and Timoshenko beam theory are less applied in the study of tunnels. This paper provides an analytical method to predict the displacements of small curved tunnels caused by deep excavation with time effects. Firstly, by introducing the fractional derivative Merchant model, a mechanical approach is proposed for analyzing the structural deformation of neighboring tunnels induced by foundation pit excavation. The parameters of viscoelastic soils are further derived in the Laplace domain based on time variability properties. Secondly, the additional stress field on existing small curvature tunnels is solved with theory of viscoelastic Mindlin solution and load reduction in foundation pits. Moreover, a deformation calculation model for curved shield tunnels is established by applying Pasternak foundation and Timoshenko beam theory. The time domain solutions for the radial and vertical deformations of small curvature tunnels are then derived by finite difference method along with Laplace positive and inverse transforms. In addition, the engineering measured data and three-dimensional numerical simulation solutions are compared with the analytical solution to verify relatively accuracy. Finally, sensitivity analyses are performed for parameters such as the buried depth of tunnels, minimum clear distance, fractional order, excavation method and creep time.

With the increasing construction of engineering structures on soft soils, accurately assessing their consolidation behavior has become crucial. To address this, Terzaghi's one-dimensional consolidation model was revisited. The elastic behavior of soil skeleton was modified by incorporating viscous effects using the fractional derivative Merchant model (FDMM), while the linear Darcy's law governing flux-pressure relations was extended by introducing time memory formalism through the fractional derivative Darcy model (FDDM). The governing equation is derived by incorporating the resulting constitutive behavior of both the soil skeleton and water flow into the Terzaghi's formulation of the poroelasticity problem. The proposed rheological consolidation model is solved by a forward time-centered space scheme (FTCS). After verifying the numerical procedure with published data, the influence of parameters on both the average degree of settlement and the pressure was comprehensively studied.

Wave propagation in an ocean site is an essential research topic in various scientific fields, such as offshore geotechnical engineering, ocean seismology, and underwater acoustics. Previous studies have considered the seabed soil as elastic or poroelastic, ignoring the viscoelastic characteristics of its solid skeleton. Based on the fractional-derivative viscoelastic theory and the modified Biot theory, considering the flow-independent viscosity related to solid skeleton, this paper proposes a generalized viscoelastic wave equation for a fluid-saturated porous medium. The equation has a flexible mathematical form to describe soil rheological properties more accurately through fractional order. On this basis, the total wave field equation of an ocean site, modeled as the fluid-poroviscoelastic-solid media, is established. Then an analytical solution for wave propagation in an ocean site subjected to obliquely incident P and SV waves is obtained, and its degeneration and extension are studied. The proposed method is comprehensively validated through experiment, analytical, and numerical methods. Finally, a parameter analysis is performed to investigate the effects of water depth, seabed properties (including viscoelastic parameters, fractional order and permeability), and incident angle on the seismic response of a poroviscoelastic seabed.

This study offers a comprehensive and advanced understanding of the torsional response of piles partially embedded in fractional-order viscoelastic unsaturated transversely isotropic soils, accurately capturing the true viscoelastic properties and particle orientation of the soil as formed during deposition. Based on Biot's threephase porous media wave equations and considering the coupling effects between the immiscible fluids (water and air) in the pores, the dynamic governing equations for fractional-order viscoelastic unsaturated transversely isotropic soil are established. The soil vibration displacement is solved using the method of separation of variables. In the frequency domain, employing the transfer matrix method and considering the continuity and boundary conditions of the pile-soil system for both the embedded and exposed portions, the analytical solution for the torsional complex impedance at the pile head of a partially embedded single pile in fractionalorder viscoelastic unsaturated transversely isotropic soil is derived. Furthermore, a semi-analytical solution for the pile head response in the time domain under half-sine pulse excitation is obtained through inverse Fourier transform and convolution theorem. Numerical examples are presented to investigate the effects of the parameters of the fractional-order viscoelastic constitutive model and the pile-soil parameters on the torsional complex impedance at the pile head.

Stiff clay exists widely in the world, but its significant time- and temperature-dependent mechanical features have not been fully modeled. In the context of fractional consistency viscoplasticity and bounding/subloading surface theory, this study proposes a novel nonisothermal fractional order two-surface viscoplastic model for stiff clays. First, by proposing a generalized plastic strain rate, the isotach viscosity is modified and extended to both over-consolidated and nonisothermal conditions that take into consideration the effects of temperature and OCR on thermal accelerated creep. Then, two strain rate and temperature-dependent yield surfaces are proposed with isotropic and progressive hardening rules to consider thermal collapse, strain rate effects, and smooth transition from elastic to viscoplastic behaviors. Next, the stress-fractional operator of the loading surface, according to the principle of fractional consistency viscoplasticity, is introduced to describe the nonassociativity of stiff clays. Finally, the predictive ability of the model is validated by simulating triaxial tests on Boom clay with various stress paths considering the temperature- and time-dependent features of stiff clays.

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 strength and dilatancy of sand are mainly influenced by the void ratio, confining pressure and stress path. In engineering, the stress-strain relationship of sand in three-dimensional stress state is complicated, where the state-dependent properties of sand are difficult to be described by traditional constitutive models. Thus, fractional plastic models based on different fractional derivatives were developed to capture such state-dependent behavior of sand. This paper attempts to make a comparative study of the fractional models based on two typical fractional derivatives, i.e., the R-L derivative and Caputo derivative. The results show that the different types of fractional derivatives are mainly reflected in the different order of differentiation and integration, which will have a significant impact on the calculation of plastic flow direction, stress-dilatancy ratio and fractional order parameter beta in the constitutive model. By determining the constitutive parameters of the two models, the constitutive behaviors predicted by different models were compared with the corresponding test results of saturated sands under different initial mean pressures and different stress paths. The models can reasonably simulate the test results of saturated sands, where the dilatancy characteristic can be captured. Compared with RL model, Caputo model can predict more volumetric strain in the dilatancy process, and has better prediction effect. Overall, the predicted effects of the two models are close, with a maximum difference of about 7 %.

We took the silt soil in the Yellow River flood area of Zhengzhou City as the research object and carried out triaxial shear and triaxial creep tests on silt soil with different moisture contents (8%, 10%, 12%, 14%) to analyze the effect of moisture content on silt soil. In addition, the influence of moisture contents on soil creep characteristics and long-term strength was analyzed. Based on the fractional derivative theory, we established a fractional derivative model that can effectively describe the creep characteristics of silt soil in all stages, and used the Levenberg-Marquardt algorithm to inversely identify the relevant parameters of the fractional derivative creep model. The results show that the shear strengths of silt soil samples with moisture contents of 8%, 10%, 12% and 14% are 294 kPa, 236 kPa, 179 kPa and 161 kPa, respectively. The shear strength of silt soil decreases with increasing moisture content. When the moisture content increases, the cohesion of the silt soil decreases. Under the same deviatoric stress, the higher the moisture content of the silt soil, the greater the deformation will be. The long-term strength of silt soil decreases exponentially with the increase of moisture content. If the moisture content is 12%, the long-term strength loss rate of silt soil is the smallest, with a value of 32.96%. The calculated values of our creep model based on fractional derivatives have a high goodness of fit with the experimental results. This indicates that our model can better simulate the creep characteristics of silt soil. This study can provide a theoretical basis for engineering construction and geological disaster prevention in silt soil areas in the Yellow River flood area.

In this paper, the one-dimensional rheological consolidation characteristics of multilayered saturated soil foundations under time-dependent loading and heating are investigated by considering the semi-permeability and the interface thermal resistance. By introducing the fractional derivative model and the thermos-elastic theory, a thermo-mechanical coupling model is established to describe the rheological properties of saturated soils. Semi-analytical solutions for strain, temperature increment, pore water pressure and settlement were derived through the Laplace transform and its inverse. The accuracy of the solutions proposed in this paper has been verified by comparing with existing solutions. The effects of different thermal contact models of the interface on the rheological properties of saturated soils under semi-permeable boundary are discussed, and the effects of fractional derivative order, constitutive material parameters, and thermal conductivity of soil on the thermal consolidation process are investigated. The results show that: neglecting the thermal resistance effect can result in an overestimates of the impact of rheological properties on the thermal consolidation process of saturated soils under semi-permeable boundaries; As the thermal resistance coefficient increases, the influence of soil thermal conductivity on settlement decreases.

Creep deformation control is the key point and difficulty in the construction of loess high fill, the creep characteristics of loess with different compactness and confining pressure conditions has been studied. To achieve the objective, the influence of different conditions on the creep deformation characteristics of loess were analyzed by the triaxial creep tests of loess under different compaction and confining pressures. The results show that the instantaneous deformation of the soil samples gradually decrease with increasing compactness, and the total creep deformation also decreases. With the increase of confining pressure, the deformation increase gradually with the compactness decreased. Finally, in order to describe the creep process of loess, the creep model suitable for different compactness is proposed, which is based on fractional calculus and the continuous damage theory. Through fitting verification, the applicability of the theoretical model to the description of loess creep characteristics is proved, and then the whole stages of loess creep can be better described.