Elastoplastic Stress-Strain Theory for Cohesionless Soil

Wei H., Yao Z., Wang X., Song Z.

Poorsolhjouy P., Mews K.S., Misra A.

Abstract Geomaterials are widely known to exhibit loading-path-dependent mechanical behavior. The path dependence becomes more evident in triaxial loading conditions where the three principal stresses can have different histories, thereby creating a rich combination of complicated loading regimes. True triaxial loading which allows for independently varying the principal stresses, therefore, is the ideal experiment to investigate this behavior. In this work, we have used the Granular Micromechanics Approach (GMA) to derive the macroscopic behavior of rock-like granular materials by studying the behavior of inter-granular contacts in all directions. The work is motivated by the recent true triaxial experiments on sandstones showing the effect of Lode angle and mean stress on the stress state at failure. In this paper, we have analyzed the experimental loading condition as well as an additional loading scenario in which both the Lode angle and the mean stress are kept constant. Our micro-mechanical analysis shows that these two loading paths result in different failure envelopes. Accordingly, a priori assumptions of the failure criteria that are based upon stress states, and only weakly on loading paths, are shown to lead to misleading results. The GMA can be used as a theoretical-numerical predictive alternative to experimental measurements for evaluating the load-path dependency of failure. Further, GMA is shown to be able to asses failure stress state as well as the failure mode based on localization analysis.

Meng F., Shi L., Hall S., Baud P., Wong T.

Zhao J., Tong H., Yuan J., Wang Y., Cui J., Shan Y.

Currently, the mechanical properties of calcareous sand are mainly studied through triaxial tests, as traditional uniaxial compression tests fail to capture real loading conditions and soil strength anisotropy. To address this, true triaxial tests were conducted to examine the effect of the intermediate principal stress parameter (b) on the three-dimensional strength and deformation behavior of calcareous sand. In the constant b and σ3 tests, as the b value increased, both the strength and peak friction angle (φps) of calcareous sand were increased, while the tangent slope of the dilatancy curve showed a gradual rise.. The φps of calcareous sand was found to be higher compared to silica sand and coarse-grained soils. In the constant mean effective stress (p) and b test, the strength was increased with higher values of both b and p. The Matsuoka-Nakai 3D strength criterion proved more effective in fitting the 3D strength of calcareous sand in π plane. As the b value increased, the critical stress ratio (Mc) was decreased. A quadratic function can better represent the Mc of calcareous sand in the π plane under varying confining pressures. Furthermore, the Mc of calcareous sand was higher than that of silica sand and completely decomposed granite soil. This study provides a valuable experimental basis for understanding the 3D strength and deformation characteristics of calcareous sand in oceanic engineering infrastructure.

Mortara G., di Prisco C.

In this paper, a new approach for rotational hardening in elastic-plasticity is formulated. After discussing the standard yield criteria employed for geomaterials and the rotational hardening models proposed in the past, the authors introduce the concept of pure rotational hardening, that is a rigid rotation of the yield surface not implying any distortion of it. In the second part of the paper, a new approach for rotational hardening, based on Householder transformations, is proposed. The method, that allows to reflect vectors with respect to a given hyper-plane, is briefly described since not usually employed in geomechanics. Moreover, the authors clarify that any yield surface or plastic potential rotation, not being a rolling, is a transformation keeping unaltered first and second invariants, but not the third. As a consequence, when rotational hardening is introduced, the use of the third mixed invariant, for defining in the deviatoric plane the yield surface shape, is not appropriate. Finally, the application of the proposed approach in the formulation of anisotropic elastic–plastic strain hardening constitutive models is briefly discussed for the classes of uncoupled and hybrid yield criteria that include a dependence of the yield surface on Lode angle.

Li J., Cao Y., Chen F., Lin Y.

Handspiker W., Liu Z., Ghafghazi M.

Constitutive models and failure criteria of soils, rocks, and other materials often need to be extended beyond the triaxial state where they are usually defined, for plane strain, axisymmetric, or three-dimensional analyses. This extension is commonly done by making the stress ratio a function of the Lode angle. This process turns two-dimensional yield, plastic potential, bounding, dilatancy and similar surfaces into three-dimensional shapes such as cones and bullets. The equations used have a range of shapes on the octahedral or π-plane between Mohr-Coulomb’s irregular hexagon and Drucker-Prager’s circle. Nine stress ratio generalization equations popular in soil mechanics are evaluated based on numerical stability, agreement with available data, and ease of implementation. The computed limits on their convexity, and the flexibility they offer in the calibration process are discussed. At the end, a new equation that satisfies all these criteria while remaining simple and easy to calibrate is proposed, implemented in a finite element model, and demonstrated to improve numerical stability and efficiency.

Qiu Z., Prabhakaran A., Ebeido A., Zheng Y.

Liu J., Li X., Xiao J., Xie Y., Xia K.

Deep rocks are typically under a true-triaxial stress state. The strength of deep rock is thus dictated by both the direction and magnitude of principal stresses. The formulation of three-dimensional strength criterion for rocks is thus essential for evaluating the stability of deep-buried rock structures. With advancements in true-triaxial experimental instrumentation, several three-dimensional strength criteria have been proposed, necessitating a systematic review and consolidation of these criteria. This review first introduces the concept of three-dimensional stress state. Subsequently, classical strength criteria such as the Mohr-Coulomb Criterion, the Hoek-Brown criterion, and the Drucker-Prager criterion are reiterated. However, these traditional strength criteria inadequately describe rock strength under true-triaxial stress conditions. To better capture the influence of intermediate principal stress, hydrostatic pressure, and Lode angle on rock strength, researchers have revised classical strength criteria. Modified strength criteria and unified strength criteria based on classical formulations are also introduced. Notably, the unified strength criterion incorporates multiple single criteria and demonstrates wider applicability. Furthermore, beyond macroscopic strength criteria, this review also discusses micromechanical strength criteria, where the stress state and crack propagation govern rock mechanical behaviors. This comprehensive review may serve as a valuable source for addressing the problem of deep rock strength in energy extraction and other rock engineering applications.

Jin Z., Liu J., Ma G., Hu C., Yang Q., Shi X., Wang X.

ABSTRACTThe contact network of granular materials is often divided into strong and weak subnetworks, which play different roles in micromechanics. Within the strong contact network, there exists the largest connected component, that is, the largest cluster, which may connect system boundaries and could be the most important structure in force transmission of the whole system. This paper concerns the particular features of the largest cluster in the strong contact network of granular materials, by considering the combining effects of loading path and particle shape. A series of true triaxial tests with various intermediate principal stress ratios are conducted for granular assemblies of different shaped particles using the discrete element method (DEM). Both the macroscopic stress–strain responses and the microscopic topological changes of the contact network are investigated. It is found that both particle shape and loading path will influence the shear strength and the topological features of the strong network. The threshold (the ratio to the average force) is used to distinguish the strong and weak networks, and a critical threshold can be identified by comparing the network‐based metrics. The largest cluster within the strong network approaching the critical threshold can span the boundaries in each direction with minimum contacts, which occupies a small portion of particles and contacts but transmits a considerable portion of the applied stress. In addition, the similar contribution weight of the largest cluster to the deviatoric stress is identified for granular materials with different particle shapes.

Raggi F., Altarejos-García L.

Deformation predictions in high Concrete Face Rockfill Dams tend to underestimate observed settlements due to scale effect and breakage phenomena that cannot be adequately captured by laboratory tests. This paper presents a Visco-Elasto-Perfectly Plastic (VEPP) model for predicting deformations in high Concrete Face Rockfill Dams (CFRDs) that addresses these challenges incorporating explicitly key rockfill parameters like grain size and post-compaction porosity, which influence both the non-linear elastic and plastic behaviors of rockfill. The VEPP model enables deformation prediction while using standard laboratory test results. The model’s effectiveness was demonstrated through its application to the 233 m high Shuibuya Dam, the tallest CFRD in the world. The VEPP model predictions closely align with observed deformations throughout the dam’s construction, impoundment, and early operational stages. By using physically meaningful parameters, the model reduces the uncertainty associated with the empirical assessment of model parameters using back-analysis from similar projects. While the VEPP model offers improved predictive accuracy, particularly during early design phases, further advancements could be achieved by refining the creep formulation and accounting for grain size evolution during construction. This approach has the potential to optimize the design and construction of future high CFRD construction.

Jamshidian M., Mansuri Zadeh M., Mohammadzadeh O., Abdideh M.

Breakdown is an important process in geomechanics; a very complex process in hydraulic fracturing which has been the subject of extensive research in the literature. There exist several models in the literature for predicting the breakdown pressure. In this research, the breakdown pressure for hydraulic fracturing in a vertical borehole was modeled using 2D and 3D failure analysis. In the geomechanical model constructed in this case study, elastic moduli were obtained using petrophysical data as well as data extracted from core analysis. The in-situ stress state of the reservoir was obtained by poroelastic horizontal strain model and was then validated by field data. To test the accuracy of the horizontal strain model, several models were used to obtain the minimum horizontals stress. At the end, the induced principal stresses inside the borehole were modeled by Kirch Equations. Four failure criteria, namely Mohr–Coulomb, 2D Hoek–Brown, Hubbert-Willis and 3D Mogi-Coulomb were used to obtain the breakdown pressure for the target reservoir. Based on the prediction results of these failure criteria, it was obtained that 2D Hoek–Brown, Hubbert-Willis, and 3D Mogi-Coulomb criteria resulted in seemingly unrealistic breakdown pressures with respect to the minimum horizontal stress gradient. The Mohr–Coulomb criterion produced lower breakdown pressure gradients, yet closer to the minimum horizontal stress values, even though it neglects the effect of intermediate stress.

Huang X., Sun Y., Sumelka W., Gao Y.

Clay and sand were often treated as two different materials that required respective constitutive models to capture the state-dependent nonassociated responses. This study developed a three-dimensional isotropic plasticity model for clay with different over-consolidation ratios (OCRs) and sand with particle breakage, through adopting shift stress-enriched loading/bounding surface, fractional flow rule and flexible critical state line, in the transformed stress space. The model was implemented in Abaqus through UMAT subroutine with an explicit adaptive substepping integration algorithm. Validation against a series of element tests on clay and sand showed that the unified model can well reproduce the stress–strain and critical state behavior of clay and sand. To further demonstrate the capability of the model, two typical boundary value problems, i.e., shear band and ground settlement, were simulated. It was found that as the shear band initiated, higher shear strain and dilatancy were accumulated within the shear band, whereas dilatancy outside the shear band ceased soon with further shearing. Ground settlement and the associated excess pore water pressure at the same consolidation time decreased with the increasing OCR, which agreed well with other studies. The simulation performances verified the capability of the unified model in resolving practical engineering problems.

An H., Mu X.

With the shallow resources dwindling, many countries have entered into deep mining one after another. Rock fracture caused by high stress mining disturbances is a significant concern. Destabilization caused by rock fracture not only diminishes productivity, but can also poses the risk of injuries and property damage. Therefore, it is of great significance to investigate the rock fracture mechanism of deep mining to ensure mining safety and improve production efficiency. This paper begins by summarizing key challenges associated with deep mining. Subsequently, it categorizes the outcomes of previous research on this issue into various themes, encompassing laboratory tests, theoretical analyses, numerical simulations and field measurement. This paper provides an overview of a number of representative studies that the growing scenarios and an increase in our understanding of this issue. A summary of the limitations of each contribution is presented, as well as the expected aspects that need to be optimized in the future research. It is found that our knowledge is far from complete, and there are still gaps to be narrowed, particularly concerning the theory of deep rock mechanics, identification of deformation and fracture in deep rock, establishment of three-dimension strength criterion, accuracy of numerical modelling and accuracy of field measurement. The review aims at providing researchers and engineers with a comprehensive understanding of the pertinent issue and guiding them for more in-depth exploration and research.

Zhang R., Zhou J., Wang Z.

Given the critical role of true triaxial strength assessment in underground rock and soil engineering design and construction, this study explores sandstone true triaxial strength using data-driven machine learning approaches. Fourteen distinct sandstone true triaxial test datasets were collected from the existing literature and randomly divided into training (70%) and testing (30%) sets. A Multilayer Perceptron (MLP) model was developed with uniaxial compressive strength (UCS, σc), intermediate principal stress (σ2), and minimum principal stress (σ3) as inputs and maximum principal stress (σ1) at failure as the output. The model was optimized using the Harris hawks optimization (HHO) algorithm to fine-tune hyperparameters. By adjusting the model structure and activation function characteristics, the final model was made continuously differentiable, enhancing its potential for numerical analysis applications. Four HHO-MLP models with different activation functions were trained and validated on the training set. Based on the comparison of prediction accuracy and meridian plane analysis, an HHO-MLP model with high predictive accuracy and meridional behavior consistent with theoretical trends was selected. Compared to five traditional strength criteria (Drucker–Prager, Hoek–Brown, Mogi–Coulomb, modified Lade, and modified Weibols–Cook), the optimized HHO-MLP model demonstrated superior predictive performance on both training and testing datasets. It successfully captured the complete strength variation in principal stress space, showing smooth and continuous failure envelopes on the meridian and deviatoric planes. These results underscore the model’s ability to generalize across different stress conditions, highlighting its potential as a powerful tool for predicting the true triaxial strength of sandstone in geotechnical engineering applications.