Size effect of fracture characteristics for anisotropic quasi-brittle geomaterials

Understanding the size effect exhibited by the fracture mechanism of anisotropic geomaterials is important for engineering practice. In this study, the anisotropic features of the nominal strength, apparent fracture toughness, effective fracture energy and fracture process zone(FPZ) size of geomaterials were first analyzed by systematic size effect fracture experiments. The results showed that the nominal strength and the apparent fracture toughness decreased with increasing bedding plane inclination angle.The larger the specimen size was, the smaller the nominal strength and the larger the apparent fracture toughness was. When the bedding inclination angle increased from 0° to 90°, the effective fracture energy and the effective FPZ size both first decreased and then increased within two complex variation stages that were bounded by the 45° bedding angle. Regardless of the inherent anisotropy of geomaterials,the nominal strength and apparent fracture toughness can be predicted by the energy-based size effect law, which demonstrates that geomaterials have obvious quasi-brittle characteristics. Theoretical analysis indicated that the true fracture toughness and energy dissipation can be calculated by linear elastic fracture mechanics only when the brittleness number is higher than 10;otherwise, size effect tests should be adopted to determine the fracture parameters.

Basic characteristics and development of yield criteria for geomaterials

The yield criteria of geomaterials play a crucial role in studying and designing the strength of materials and structures.The basic characteristics of yield criteria for geomaterials need to be studied under the framework of continuum mechanics.These characteristics include the effects of strength difference（SD） of materials in tension and compression,normal stress,intermediate principal stress,intermediate principal shear stress,hydrostatic stress,twin-shear stresses,and the convexity of yield surface.Most of the proposed yield criteria possess only one or some of these basic characteristics.For example,the Tresca yield criterion considers only single-shear stress effect,and ignores the effect of SD,normal stress,intermediate principal stress,intermediate principal shear stress,hydrostatic stress,and twin-shear stresses.The Mohr-Coulomb yield criterion accounts for the effect of SD,normal stress,single-shear stress and hydrostatic stress,but disregards the effect of intermediate principal stress,intermediate principal shear stress,and twin-shear stresses.The basic characteristics remain to be fully addressed in the development of yield criterion.In this paper,we propose a new yield criterion with three features,that is,newly developed,better than existing criteria and ready for application.It is shown that the proposed criterion performs better than the existing ones and is ready for application.The development of mechanical models for various yield criteria and the applications of the unified strength theory to engineering are also summarized.According to a new tetragonal mechanical model,a tension-cut condition is added to the unified strength theory.The unified strength theory is extended to the tension-tension region.

CONSTITUTIVE THEORY OF PLASTICITY COUPLED WITH ORTHOTROPIC DAMAGE FOR GEOMATERIALS

Constitutive theory of plasticity coupled with orthotropic damage for geomaterials was established in the framework of irreversible thermodynamics. Prime results include I evolution laws are presented for coupled evolution of plasticity and orthotropic damage 2) the orthotropic damage tensor is introduced into the Mohr-Coulomb criterion through homogenization. Both the degradation of shear strength and degradation of friction angle caused by damage are included in this model. The dilatancy is calculated with the so-called damage strain.

Some micromechanical models of elastoplastic behaviors of porous geomaterials

Some micromechanics-based constitutive models are presented in this study for porous geomaterials.These micro-macro mechanical models focus on the effect of porosity and the inclusions on the macroscopic elastoplastic behaviors of porous materials. In order to consider the effect of pores and the compressibility of the matrix, some macroscopic criteria are presented firstly for ductile porous medium having one population of pores with different types of matrix(von Mises, Green type, Misese Schleicher and Druckere Prager). Based on different homogenization techniques, these models are extended to the double porous materials with two populations of pores at different scales and a Druckere Prager solid phase at the microscale. Based on these macroscopic criteria, complete constitutive models are formulated and implemented to describe the overall responses of typical porous geomaterials(sandstone,porous chalk and argillite). Comparisons between the numerical predictions and experimental data with different confining pressures or different mineralogical composites show the capabilities of these micromechanics-based models, which take into account the effects of microstructure on the macroscopic behavior and significantly improve the phenomenological ones.

Large deformation simulations of geomaterials using moving particle semi-implicit method

Numerical simulation tools are required to describe large deformations of geomaterials for evaluating the risk of geo-disasters. This study focused on moving particle semi-implicit(MPS) method, which is a Lagrangian gridless particle method, and investigated its performance and stability to simulate large deformation of geomaterials. A calculation method was developed using geomaterials modeled as Bingham fluids to improve the original MPS method and enhance its stability. Two numerical tests showed that results from the improved MPS method was in good agreement with the theoretical value.Furthermore, numerical simulations were calibrated by laboratory experiments. It showed that the simulation results matched well with the experimentally observed free-surface configurations for flowing sand. In addition, the model could generally predict the time-history of the impact force. The MPS method could be a useful tool to evaluate large deformation of geomaterials.

Describing failure in geomaterials using second-order work approach

Geomaterials are known to be non-associated materials. Granular soils therefore exhibit a variety of failure modes, with diffuse or localized kinematical patterns. In fact, the notion of failure itself can be confusing with regard to granular soils, because it is not associated with an obvious phenomenology. In this study, we built a proper framework, using the second-order work theory, to describe some failure modes in geomaterials based on energy conservation. The occurrence of failure is defined by an abrupt increase in kinetic energy. The increase in kinetic energy from an equilibrium state, under incremental loading, is shown to be equal to the difference between the external second-order work,involving the external loading parameters, and the internal second-order work, involving the constitutive properties of the material. When a stress limit state is reached, a certain stress component passes through a maximum value and then may decrease. Under such a condition, if a certain additional external loading is applied, the system fails, sharply increasing the strain rate. The internal stress is no longer able to balance the external stress, leading to a dynamic response of the specimen. As an illustration, the theoretical framework was applied to the well-known undrained triaxial test for loose soils. The influence of the loading control mode was clearly highlighted. It is shown that the plastic limit theory appears to be a particular case of this more general second-order work theory. When the plastic limit condition is met, the internal second-order work is nil. A class of incremental external loadings causes the kinetic energy to increase dramatically, leading to the sudden collapse of the specimen, as observed in laboratory.

Constitutive modeling for mechanical behaviors of geomaterials, newdesigns and techniques in geotechnical engineering

This Special Issue of the Journal of Rock Mechanics and GeotechnicalEngineering （JRMGE） contains 13 papers prepared by internationalexperts on various general topics in geomechanics, rockmechanics and geotechnical engineering. It represents a usefulmix of theoretical developments, testing and practical applications.We present in the following brief details in the papers, alphabeticallyin accordance with the last name of the first author.Barla presents a review of tunneling techniques with emphasison the full-face method combining full-face excavation and facereinforcement by means of fiber-glass elements with a yieldcontrolsupport. This method has been used successfully in difficultgeologic conditions, and for a wide spectrum of ground situations.The validation of the method with respect to the Saint Martin LaPorte access adit along the LyoneTurin Base tunnel experiencingseverely squeezing conditions during excavation is also includedin the paper. The numerical modeling with consideration of therock mass time-dependent behavior showed a satisfactory agreementwith monitoring results.

A thermodynamics-based three-scale constitutive model for partially saturated granular materials

A three-scale constitutive model for unsaturated granular materials based on thermodynamic theory is presented.The three-scale yield locus,derived from the explicit yield criterion for solid matrix,is developed from a series of discrete interparticle contact planes.The three-scale yield locus is sensitive to porosity changes;therefore,it is reinterpreted as a corresponding constitutive model without phenomenological parameters.Furthermore,a water retention curve is proposed based on special pore morphology and experimental observations.The features of the partially saturated granular materials are well captured by the model.Under wetting and isotropic compression,volumetric compaction occurs,and the degree of saturation increases.Moreover,the higher the matric suction,the greater the strength,and the smaller the volumetric compaction.Compared with the phenomenological Barcelona basic model,the proposed three-scale constitutive model has fewer parameters;virtually all parameters have clear physical meanings.

A THERMO-PLASTIC/VISCOPLASTIC DAMAGE MODEL FOR GEOMATERIALS

A thermo-plastic/viscoplastic damage coupled model was formulated to describe the time independent and time dependent behaviors of geomaterials under temperature effect. The plastic strain was divided into instantaneous plastic strain and creep plastic strain. To take temperature effect into acconnt, a temperature variable was introduced into the instantaneous and creep plastic behavior descriptions and damage characterization, and a linear thermal expansion law was used in constitutive equation formulation. According to the mechanical behavior of rock salt, a specific model was proposed based on the previous model and applied to Avery rock salt, in which the numerical results obtained from our model had a good agreement with the data from experiments.

Strength-increase mechanism and microstructural characteristics of a biotreated geomaterial

Microbially induced calcite precipitation(MICP)is a recently proposed method that is environmentally friendly and has considerable potential applications in artificial biotreated geomaterials.New artificial biotreated geomaterials are produced based on the MICP technology for different parent soils.The purpose of this study is to explore the strength-increase mechanism and microstmctural characteristics of the biotreated geomaterial through a series of experiments.The results show that longer mineralization time results in higher-strength biotreated geomaterial.The strength growth rate rapidly increases in the beginning and remains stable afterwards.The calcium ion content significantly increases with the extended mineralization time.When standard sand was used as a parent soil,the calcium ion content increased to a factor of 39 after 7 days.The bacterial cells with attached calcium ions serve as the nucleus of crystallization and fill the pore space.When fine sand was used as a parent soil,the calcium ion content increased to only a factor of 7 after 7 days of mineralization.The nucleus of crystallization could not normally grow because of the limited pore space.The porosity and variation in porosity are clearly affected by the parent soil.Therefore,the strength of the biotreated geomaterial is affected by the parent soil properties,mineralization time,and granular material pore space.This paper provides a basis for theory and experiments for biotreated geomaterials in future engineering practice.

Several basic problems in plastic theory of geomaterials

Based on the basic mechanical properties of geomaterials,it was proven that the Drucker Postulate and the classical theory of plasticity can not be applied to geomaterials.Moreover,several basic problems of plastic theory of geomaterials were discussed.Based on the strict theoretical analysis,the following have been proven:the single yield surface model based on the classical theory of plasticity is unsuitable for geomaterials whether the rule of associated flow is applied or not;the yield surface of geomaterials is not unique,and its number is the same as the freedoms of plastic strain increment;the yield surface is not convex;and the rule of associated flow is unsuitable for geomaterials.

Simulation of dilatancy-controlled gas migration processes in saturated bentonite using a coupled multiphase flow and elastoplastic H2 M model

Dilatancy-controlled gas flow in preferential pathways plays a key role in the safety analysis of radioactive waste repositories.This is particularly the case for bentonite,an often-preferred barrier material.Gas flow in preferential pathways is characterized by localization and spontaneous behavior,which is challenging to simulate in numerical models due to strong hydro-mechanical coupling.To analyze a laboratory experiment in the framework of the DECOVALEX-2023 project,this study introduced a new approach of combining continuous modelling methods with spatial material properties derived from material heterogeneities and experimental observations.The proposed model utilized hydro-mechanical spatial distributions,namely Young’s modulus and gas entry pressure,and elastoplasticity combined with a linear swelling model.A conceptual strain-dependent permeability approach simulated dilatancycontrolled gas flow based on hydro-mechanical coupling.To test the effectiveness of the presented approach,a gas injection test in a compacted,saturated bentonite sample was simulated using the opensource code OpenGeoSys 5.8 and compared with experimental observations.The presented methodology is capable of simulating localized gas flow in preferential pathways.The spatial distributions of Young’s modulus and gas entry pressure affect the swelling pressure,relative permeability and,in combination with the strain-dependent permeability model,also the intrinsic permeability.

Rock and Soil Classification Using PLS-DA and SVM Combined with a Laser-Induced Breakdown Spectroscopy Library

Laser-induced breakdown spectroscopy （LIBS） has become a powerful technology in geological applications. The correct identification of rocks and soils is critical to many geological projects. In this study, LIBS database software with a user-friendly and intuitive interface is developed based on Windows, consisting of a database module and a sample identification module. The database module includes a basic database containing LIBS persistent lines for elements and a dedicated geological database containing LIBS emission lines for several rock and soil reference standards. The module allows easy use of the data. A sample identification module based on partial least squares discriminant analysis （PLS-DA） or support vector machine （SVM） algorithms enables users to classify groups of unknown spectra. The developed system was used to classify rock and soil data sets in a dedicated database and the results demonstrate that the system is capable of fast and accurate classification of rocks and soils, and is thus useful for the detection of geological materials.

Influence of particle contact models on soil response of poorly graded sand during cavity expansion in discrete element simulation

The discrete element method(DEM) has been extensively adopted to investigate many complex geotechnical related problems due to its capability to incorporate the discontinuous nature of granular materials. In particular, when simulating large deformations or distortion of soil(e.g. cavity expansion),DEM can be very effective as other numerical solutions may experience convergence problems. Cavity expansion theory has widespread applications in geotechnical engineering, particularly to the problems concerning in situ testing, pile installation and so forth. In addition, the behaviour of geomaterials in a macro-level is utterly determined by microscopic properties, highlighting the importance of contact models. Despite the fact that there are numerous contact models proposed to mimic the realistic behaviour of granular materials, there are lack of studies on the effects of these contact models on the soil response.Hence, in this study, a series of three-dimensional numerical simulations with different contact constitutive models was conducted to simulate the response of sandy soils during cylindrical cavity expansion. In this numerical investigation, three contact models, i.e. linear contact model, rolling resistance contact model,and Hertz contact model, are considered. It should be noted that the former two models are linear based models, providing linearly elastic and frictional plasticity behaviours, whereas the latter one consists of nonlinear formulation based on an approximation of the theory of Mindlin and Deresiewicz. To examine the effects of these contact models, several cylindrical cavities were created and expanded gradually from an initial radius of 0.055 m to a final radius of 0.1 m. The numerical predictions confirm that the calibrated contact models produced similar results regarding the variations of cavity pressure, radial stress, deviatoric stress, volumetric strain, as well as the soil radial displacement. However, the linear contact model may result in inaccurate predictions when highly angular soil particles are involved. In addition, considering the excessive soil displacement induced by the pile installation(i.e. cavity expansion), a minimum distance of11 a(a is the cavity radius) is recommend for practicing engineers to avoid the potential damages to the existing piles and adjacent structures.

Mapping urban underground potential in Dakar,Senegal:From the analytic hierarchy process to self-organizing maps

This article presents a mapping method that seeks to provide urban planning with a diagnostic overview of the underground resources of an urban area.Resource potentials(for buildable space,groundwater or geomaterial extraction and geothermal energy)tend to be investigated on a needs-only basis once a project or plan has already been elaborated.This paradigm of‘needs to resources’risks favoring single-use rather than multi-use underground development,leading to unforeseen conflicts between possible uses(e.g.,pollution of an aquifer or congestion of infrastructure)or the irreversible loss of potential synergies(e.g.,geothermal collectors on building foundations).The Deep City project at the EPFL in Switzerland has been working on an alternative paradigm of‘resources to needs’,which is a holistic approach addressing the underground as a source of opportunity in synergy with surface development for curtailing urban sprawl while preserving public places or parks.The method,which combines geological and surface urban data,produces maps of individual and combined resource potentials without prioritizing any particular planning objective.This communication will present the method and the resulting maps through a case study conducted in 2016 in the city of Dakar,Senegal.After first summarizing the Deep City project and the mapping method,the urban and geological conditions of Dakar will be presented,followed by the application and results of the Deep City method.The calculation of the combined potentials map is an opportunity to compare two alternative methods of combination,the Analytic Hierarchy Process and Self-Organizing Maps(SOMs).Although the mapping method does not require complicated data collection or analysis,the SOM may be better suited both for dealing with larger quantities of data and for providing more meaningful mappings of geological and urban data in three dimensions.