This paper presents a constitutive model for biotreated sand, developed within the framework of thermodynamic theory, to describe its mechanical behavior under undrained shear conditions. The model incorporates a reinforcement index and a hardening index to account for bonding effects. Undrained triaxial shear tests are conducted to validate the constitutive model. The results demonstrate the model's capacity to accurately predict the undrained shear behavior of biotreated sand under various reinforcement levels and initial confining pressures. It effectively captures the evolution of deviatoric stress, pore pressure, and stress paths. Furthermore, the model accounts for energy dissipation and the degradation of inter-grain bonding during undrained shearing, providing a theoretical foundation for the engineering application of biotreated sand.

A novel thermo-hydro-mechanical-chemical (THMC) coupling model grounded in thermodynamic dissipation theory was established to unravel the intricate behavior of unsaturated sulfate-saline soils during cooling crystallization. The model quantifies energy transfer and dissipation during crystallization and introduces a method to calculate the amount of sulfate crystallization. It intricately captures the interdependencies between crystallization, pore water pressure, crystallization pressure and volumetric expansion, while also accounting for the dynamic feedback of latent heat from phase transitions on heat conduction. The reliability of the model was validated through experimental data. Numerical simulations explored the effects of cooling paths, thermal conductivity, initial salt content and initial porosity on the crystallization behavior and mechanical properties. The model provides theoretical support for optimizing the engineering design and facility maintenance of sulfatesaline soils.

In-depth research on the mechanical properties and constitutive models of gas hydrate-bearing sediments (GHBSs) is fundamental for achieving efficient hydrate exploration and geological disaster prevention. In the current study, a bounding surface model for GHBSs is developed based on the principle of thermodynamics. By choosing an appropriate dissipation function and free energy function, a yield surface function containing three shape parameters can be obtained. Considering the filling and bonding effects of hydrates, and introducing the hydrate strength evolution parameter, a thermodynamics-based bounding surface model for GHBSs is established using a non-associated flow rule. Then, the explicit substeping scheme with error control is implemented to develop a UMAT subroutine for the proposed model and integrated into the ABAQUS. Compared with the drained monotonic triaxial shear data indicates that the proposed model can adequately capture the shear behaviors of sandy, silty sandy, and clay-silty GHBSs under different stress levels and saturations. In addition, the model demonstrates good applicability and feasibility in undrained cyclic triaxial shear tests and boundary value problem analysis.

This study investigates the freezing process and mechanical impact behavior of saturated soil to provide new insights into soil thermodynamic and improve its comprehensive investigation under a cryogenic engineering environment. The unfrozen water content is a major focus of study during soil freezing. Many studies have proposed models for calculating the unfrozen water content in frozen and unfrozen pores. However, they lack uniformity and consistency on a physical basis and mathematical derivation. An unified theoretical model was derived based on the principle of thermodynamic equilibrium. The main theoretical results indicated that the dimensionless total volume of the unfrozen water membrane in the frozen pores first increased and then decreased with increasing temperature, revealing the temperature effect on the unfrozen water content in frozen pores. By combining the theoretical model with the distinct element method (DEM), water freezing into ice in saturated soil was numerically simulated using two modes of particle expansion. One of the two modes proposed by the authors was to change the coefficient of expansion during saturated soil freezing to further consider the non-linear variation in unfrozen water content. Subsequently, the effects of the two modes on crack generation during saturated soil freezing were compared and analyzed. Finally, based on the dissipation energy produced in particle contacts, a method for calculating the rises in impact temperature in different particles was proposed for revealing the local and discrete changes in frozen saturated soil under impact loading. The main numerical results indicated that the proportion of the number of particles for different temperature rise ranges followed a Weibull distribution, and the average temperature rise of the particles near the incident end was higher than that of the particles near the transmission end.

More attention has been paid to integrating existing knowledge with data to understand the complex mechanical behaviour of geomaterials, but it incurs scepticism and criticism on its generalizability and robustness. Moreover, a common mistake in current data-driven modelling frameworks is that history internal state variables and stress are known upfront and taken as inputs, which violates reality, overestimates model accuracy and cannot be applied to modelling experimental data. To bypass these limitations, thermodynamically consistent hierarchical learning (t-PiNet) with iterative computation is tailored for identifying constitutive relations with applications to geomaterials. This hierarchical structure includes a recurrent neural network to identify internal state variables, followed by using a feedforward neural network to predict Helmholtz free energy, which can further derive dissipated energy and stress. The thermodynamic consistency of t-PiNet is comprehensively validated on the synthetic data generated by von Mises and modified Cam-clay models. Subsequently, the potential of t-PiNet in practice is confirmed by applying it to experiments on kaolin clay. The results indicate neural networks embedded by thermodynamics perform better on the loading space beyond the training data compared with the conventional pure neural network-based modelling method. t-PiNet not only offers a way to identify the mechanical behaviour of materials from experiments but also ensures it is further integrated with numerical methods for simulating engineering-scale problems.

A thermodynamics-based constitutive model predicting the critical state behavior of sands is developed in this paper. The model includes hyperelastic and plastic constitutive relations derived from thermodynamics. Using the concept of elastic potential, hyperelastic relations are derived to describe the stress- and -density dependency of the elastic stiffness of sands, which naturally lead to the elastic limit with stress-induced anisotropy in effective stress space. The plastic constitutive relations coupled with the nonlinear hyperelasticity are then derived based on the energy dissipations and the second law of thermodynamics. The model is capable of predicting the critical state behavior of sands without concepts of yield surface and plastic potential surface. The model is validated by predicting the undrained shear behavior of Toyoura sand. The modeling results show that different patterns of undrained shear response, such as the pure dilation type, the contraction-dilation type with hardening, the contraction-dilation type with softening, and the pure contraction type, can be well captured by the model, depending on the confining pressure and the void ratio. The distinctions of contraction/dilation and critical state behavior between triaxial compression and extension are also predicted. It is shown that the critical state behavior of sand is the combined results of the pressure/density/path-dependent hyperelasticity and plasticity coupled with each other.

Establishing a constitutive model that reflects the local bonding breakage process has always been a core task in soil mechanics and is crucial for solving engineering stability issues. Based on thermodynamic principles and breakage mechanics, this paper proposes a macro-micro thermodynamic constitutive model. This model quantitatively describes the thermodynamic behavior of local bonding breakage and the non-uniform distribution of stress-strain at the microscale. It improves the prediction accuracy of the model for deformation characteristics, which is similar to the Cambridge model in mathematical form. Firstly, based on the law of conservation of thermodynamic energy, the mathematical expression of structural breakage work during compression deformation was determined. It was found that the dissipated energy of breakage can be mainly divided into two parts: the frictional effect between bonded elements and frictional elements, and the irreversible transformation from bonded elements to frictional elements. Furthermore, a macro-micro constitutive model framework considering the thermodynamic behavior of local bonding breakage was established. Secondly, based on the constitutive framework and the deformation mechanism of loess (frictional, bonded, and damaged), the expressions for free energy, dissipated energy, and damage dissipated energy were determined. The damage yield function and elastic-plastic constitutive model considering the evolution laws of volume breakage and shear breakage were derived. Finally, the established model was used to predict the experimental data of other scholars, and its rationality and simulation advantages were verified through comparison. This model aligns better with thermodynamic principles, and its parameters are easy to determine.

The effects of cyclic heat treatments on the fracture shear behaviors are rarely reported. To enhance our understanding, granite fractures having almost the same roughness were first exposed to cyclic heating at 400 degrees C and air-cooling treatments, and then direct shear tests were performed under four levels of normal loading. The influences of thermal cycles on roughness degradation and shear properties are analyzed. The roughness degradation in the joint roughness coefficient and the three-dimensional (3D) roughness metric exhibit linear increasing tendency with increasing thermal cycles. Typical fracture shear properties, including cohesion and friction angle, peak and residual shear strength, peak and residual shear displacement, and initial and secant shear stiffness, fluctuate generally within the first 10 thermal cycles, followed by gradual decreasing tendencies. The thermal effect on the shear properties become weaker as the number of heat treatments increases from 10 to 80. Nonuniform expansion and shrinkage of mineral grains after thermal treatments produce micro-cracks within the rock matrix and on the rock surface, suggesting that asperities are easier to be sheared-off. Thermal alteration in fracture peak-shear strength could be attributed to the deterioration in rock strengths and the mismatch in opposing fracture walls. The observations would provide better insights into rock friction after high temperatures in geothermal energy exploitation. (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/).

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.

Artificial ground freezing technology is the most important construction method of complex water-bearing soft clay rock. The thermodynamic properties of soft clay rock are important evidence for the design and construction of space resources development, and the variable hydrothermal parameter can directly affect the uncertain thermodynamic properties of soft clay rock. In this work, an array of field experiments on the soft clay rock are carried out, and the anisotropic spatial variations of hydrothermal parameters of soft clay rock are obtained. The statistical variability characteristics of variable hydrothermal parameters are estimated. A stochastic coupling model of soft clay rock with heat conduction and porous flow is proposed, and the uncertain thermodynamic properties of soft clay rock are computed by the self-compiled program. Model validation with the experimental and numerical temperatures is also presented. According to the relationship between anisotropic spatial variations and statistical variability characteristics for the different random field correlation models, the effects of the autocorrelation function, coefficient of variation, and autocorrelation distance of variable hydrothermal parameters on the uncertain thermodynamic properties of soft clay rock are analyzed. The results show that the proposed stochastic analysis model for the thermal characteristics of soft clay rock, considering the spatial variability of frozen soil layers, is scientifically reasonable. The maximum standard deviation of average thickness is 2.33 m, and the maximum average temperature is 2.25 degrees C. For the autocorrelation function, the most significant impact comes from DBIN. For the coefficient of variation, the most significant impact comes from thermal conductivity. Different variations of hydrothermal parameters have different effects on the standard deviation of soft clay rock temperature. The biggest influence is the thermal conductivity, while the lowest influence is the specific heat capacity.