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.

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.

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.

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.

Laboratory description of clay normally distinguishes the scale of atoms from the scale of clay particles and aggregates. Contemporary constitutive models for clay tend to ignore this scale separation, and rather focus on phenomenology. By considering scale separation, this paper introduces a robust physics-based phenomenological constitutive model for clay that qualitatively captures their broad spectrum of rate-dependent mechanical features. The model is derived using the thoroughly rigorous hydrodynamic procedure. While some imagine that by considering rigour and physics, their models would get complicated, the resulting set of equations reveal a surprising degree of simplicity. The derivation strongly benefits from the principle of two-stage irreversibility, which describes energy flow within the material from the continuum scale down to the atomistic micro-scale, through the meso-scale of clay aggregates. While thermal and meso-related temperatures capture atomistic and clay aggregate fluctuating motions, a sink term from the latter to the former underpins the direction of the energy flow. The model's standout feature is in pinpointing new transport coefficients that drive both volumetric and shear plastic flows in a thermodynamically coupled manner. A novel scheme is then proposed to calibrate these coefficients from conventional steady-state observations. Thanks to the formulation the model shows a remarkable level of predictiveness, despite being relatively simple mathematically. In particular, the model readily explains the broad spectrum of rate-dependent phenomena during transient loading, along with creep and relaxation processes. Given the generality of hydrodynamics, it is anticipated that the new model could be expanded to capture fluid-solid transitions between liquid-like soft mud and plastic-like stiff clay responses, contingent on water content variations.

The existing traditional creep models have obvious shortcomings when describing the accelerated creep properties of the viscoplastic stage of rock. As a way to describe the whole process of rock creep and different creep stages and characterize the deformation characteristics of the accelerated creep stage, the creep damage during the creep loading process can be considered to be caused by the development of internal defects in the rock and soil materials. According to the theory of internal variable thermodynamics, the internal variable evolution equation in the form of self -consistent differential equations is established. The creep curve of rock under different temperatures is in good agreement with the model curve. But there are some errors. This is due to the inevitable differences between the samples. However, the changing trend of strain and creep time is the same. Therefore, the rock creep model established in this paper is reasonable and feasible to describe the creep characteristics under different stresses and different temperatures. The variation of the rock creep model curve under different parameters is analyzed. Then, the clear physical meaning of different parameters is obtained. Finally, the established rock creep model can predict the creep deformation under different temperatures and stress. It has theoretical significance for practical engineering.

Clays exhibit complex mechanical behaviour with significant viscous, nonlinear, and hysteric characteristics, beyond the prediction capacity of the well-known modified cam clay (MCC) model. This paper extends the MCC model to address these important limitations. The proposed family of models is constructed entirely within the hyperplasticity framework deduced from thermodynamic extremal principles. More specifically, the previously developed MCC hyper-viscoplastic model based on the isotache concept is extended to incorporate multiple internal variables and to capture recent loading history, hysteresis, and smooth response of the material. This is achieved by defining an inelastic free energy and an element that implements a bounding surface within hyperplasticity, resulting in pressure dependency in both reversible and irreversible processes with a unique critical state envelope, and only eight material parameters with a readily measurable viscous parameter. A kinematic hardening in the logistic differential form in stress space is derived that enables the proposed model to function effectively across a wide range of stresses. Based on this kinematic hardening rule, the current stress state acts as an asymptotic attractor for the back/shift stresses whose evolution rates are proportional to their current state.

A thermodynamic constitutive model for structured and destructured clays is proposed in this paper based on thermodynamic principles on the energy storages and dissipations. The model includes state-dependent relations of hyperelasticity and plasticity without the concept of yielding surface. The proposed nonlinear hyperelasticity is dependent on the sates of soil stress, density, and structure and leads to the limit state surface that varies with the bonding structure from a curved surface for structured clays to a plane surface for destructured clays. The plastic and destructure laws are subjected to the second thermodynamic law and expressed in the elastic-strain space instead of the stress space, which naturally account for the couplings between elasticity and plasticity with the Lode-angle and structure effects. The model is well validated by the predictions of drained/undrained conventional and true triaxial shearing tests for both structured and destructured clays, which well capture the K0 effect, the non-coaxiality between stress and strain, and the structure/destructure effects on the elasticstiffness and strain-softening of clays. For both structured and destructured clays, the critical-state elastic strain is unique under a fixed Lode angle and hence the critical state only relies on the critical-state density and the direction of shearing path.