Microbial induced carbonate precipitation (MICP) is a promising method for improving the performance of geotechnical engineering materials. However, there has been limited research on the creep characteristics of expansive soil treated with MICP. Therefore, this study investigated the improvement of consolidation creep characteristics of expansive soils using the MICP method through one-dimensional consolidation creep tests. The microstructure of the treated soil was examined by scanning electron microscopy (SEM) and X-ray diffraction (XRD) analysis. The results indicate that the MICP method effectively enhances the resistance of expansive soil to creep deformation. Compared to untreated expansive soil, the creep deformation of the treated soil decreased by 3.85%, 22.62%, and 18.40% for cementation solution contents of 50 mL, 100 mL, and 150 mL, respectively. Additionally, the creep curve of the improved expansive soil exhibits significant nonlinear characteristics. The creep process of the improved expansive soil can be divided into three stages: instantaneous deformation, decay creep, and stable creep. SEM images and XRD patterns reveal that the calcium carbonate precipitates generated during the MICP process can wrap, cement, and fill the voids between soil particles, which is the fundamental reason why the MICP method improves the deformation resistance of expansive soil. On the basis of the creep test results, a fractional-order creep model for MICP-treated expansive soil was established. Compared to traditional integer-order creep model, the fractional creep model can more accurately describe the entire process of consolidation creep of expansive soil improved by MICP method. The findings of this study provide a theoretical basis for analyzing the deformation of MICP-treated expansive soil under long-term loads.

This study presents the development of an isothermal model for characterising the stress-strain behaviour of clay, in the framework of thermomechanical restrictions. Clay is assumed to be a decoupled material, where the accumulation of the Helmholtz free energy can be decoupled into two components, elastic and plastic, that result in the explicit definitions of the shift and dissipative stress tensors, respectively. An anisotropic yielding function fulfilling the first and second laws of thermodynamics is then derived from the rate of plastic dissipation, where the loading tensor and fractional plastic flow tensor are also obtained. A compression-and-shearing hardening mechanism is introduced by further evaluating the thermodynamic restrictions of the rate of Helmholtz free energy at critical state. The developed model contains seven constitutive parameters, where the identification methods are discussed. Finally, an application of the developed model to simulate the drained and undrained stress-strain responses of different clays are provided.

Establishment of a creep model is an important method to analyze the relationship between soil creep deformation and time, and the element model is widely used for studying soil creep. However, the element creep model is employed for fitting saturated soil, and the mechanical element model is generally linear, which cannot well fit the nonlinear deformation of the soil with time in practice. The creep process of the soil is not only time-dependent, but also related to the deviatoric stress level. Therefore, the fractional calculus theory and a parameter n reflecting the effect of deviatoric stress level on the creep properties of the soil were introduced into the element model, and the fractional qBurgers creep model was established by using the fractional Koeller dashpot and Caputo fractional calculus. The proposed model was used to fit the triaxial test data of reticulated red clay under different net confining pressures and matric suctions by unsaturated triaxial apparatus. The proposed model can well describe the nonlinearity of unsaturated reticulated red clay, has memory and global correlation to the creep development process of unsaturated reticulated red clay, and has clear physical meaning. The functional relationships of the model parameters with the matric suction, net confining pressure and deviatoric stress level were deduced, so that the creep curves of unsaturated reticulated red clay can be obtained for any conditions, which is of great value for the study of unsaturated soils. (c) 2024 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/ 4.0/).

The study of the mechanical properties of frozen saline soil is one of the key issues in addressing the design of infrastructure in cold regions. This research focuses on the supersulfated saline soil of the Ningxia Yellow River Irrigation Area in China, conducting triaxial tests under negative temperatures (-5, -10, -15 degrees C, and - 20 degrees C) with varying water contents (12%, 16%, 20%). Based on fractional calculus theory and incorporating an exponential decay factor, this study proposes a novel fractional-order constitutive model for a unified description of the softening and hardening behaviors in frozen saline soil. The model treats frozen saline soil as a composite blend of ideal solids and ideal fluids in varying proportions, taking into account the material's inherent timedependency and non-linear stress-strain relationships. Finally, the validity of the model is verified by the calculated values of the model and the triaxial tests. The results indicate that, based on preliminary judgment, due to the presence of salt solutes, a large amount of liquid water remains in the supersulfated saline soil at temperatures ranging from 0 to -10 degrees C, forming an unstable state called warm frozen saline soil. The mechanical properties of frozen saline soil depend on the relative content of unfrozen water, ice crystals, and salt crystals and the formation of ice and salt crystals significantly enhances the strength of frozen saline soil. The computational results of the improved fractional constitutive model align well with experimental results, effectively describing the stress-strain relationship of frozen supersulfate saline soil. In the model, the parameter functions analogously to an elastic modulus and exhibits a linear relationship with temperature, and the parameter alpha characterizes the strain hardening of saline soil, while beta describes its softening behavior. The proposed fractional constitutive model, with only three parameters having clear physical significance, is convenient for practical engineering applications.

The long-term dynamic characteristics of frozen soil are important theoretical basis for the dynamic stability evaluation of geoengineering in cold regions. Compared to unfrozen soil, the dynamic creep behaviour is more complicated owing to its rheological property. In this study, triaxial tests under cyclic loads with different constant stress amplitudes and confining pressures for frozen silty clay (FSC) are carried out. The long-term dynamic creep process and deformation mechanism under different dynamic stress amplitudes were investigated. The test results show that with the cyclic numbers increasing, the dynamic elastic modulus and the hysteretic loop area decrease because of the damage accumulation in the samples. Also the dynamic strength decreases with an increase in failure cyclic numbers under different confining pressures. Based on the fractional calculus theory, replacing the Newton's dashpot in the traditional Maxwell model with fractional Abel's dashpot, a fractional dynamic creep model is established. Considering the melting and crushing of the ice inclusion, the slip effect in frozen soil is increasingly significant, the viscosity coefficient of dashpot element is decreasing with an increase in loading time. In the proposed model, a non-constant dashpot element is introduced to clarify the constitutive relation of the FSC in the accelerated creep stage. The comparison results confirm that the proposed constitutive model is valid and suitable for reflecting the long-term dynamic creep behaviours of the FSC.