Must critical state theory be revisited to include fabric effects?

Critical state (CS) is a physically observed state of granular materials at failure, based on which the critical state theory (CST) was founded. CST attempts to describe analytically the material response when CS failure occurs and constitutes the framework within which constitutive modeling techniques have been developed in the last half-century. The conditions of CST defined as necessary and sufficient to characterize CS do not include fabric orientation of material samples. In the present work, this absence of fabric is discussed in light of a newly developed anisotropic critical state theory (ACST) that enhances the classical CST by introducing an additional condition that fabric must satisfy at CS. The use of ACST framework in constitutive modeling is presented in a generic way, usable in conjunction with various constitutive models that comply with CST. Answers to some fundamental questions are attempted or suggested, e.g., as to whether the conditions of classical CST are necessary and sufficient for CS to occur, whether the ACST is simply a convenient supplement to CST or a necessary enhancement, and if the latter is true, the merits and open questions that arise. The presentation focuses on the justification and thoughts behind the proposed specific features of ACST, provides clarifications not made before, while several suggestions and disclaimers are made, and alternate approaches are proposed for further investigations on the subject matter.     

Autonomic visiting in digital 3D scenes

Human-machine interactive visiting and fixed-route visiting are currently the main roaming modes in digital three-dimensional (3D) scenes. However, in general, when a person visits an attraction area, s/he does not follow a fixed path, but instead wander about according to his/her interests. Here, we propose a new roaming mode, called autonomic visiting. That is, in a digital 3D scene, a user selects several interest spots, then a route connecting these spots can be automatically determined and 3D scene can be seen along this route. This study presents a technical approach that enables the realization of autonomic visiting in 3D scenes. Firstly, Delaunay triangular meshes for the terrain in 3D scene are established. Secondly, a plane-growth algorithm and a line-connection algorithm are introduced to automatically mend the broken parts of these triangular meshes. Thirdly, the triangular meshes are then merged and differently weighted according to different layers. Finally, a progress-zone transmission algorithm is presented to optimal the shortest route, which is derived from A-Star (A*) algorithm. Digital 3D campus of Nanjing University, China, is taken as the experimental materials. The experimental results prove the effect of the proposed approach.     

An experimental database for the development,calibration and verification of constitutive models for sand with focus to cyclic loading: part I—tests with monotonic loading and stress cycles

For numerical studies of geotechnical structures under earthquake loading, aiming to examine a possible failure due to liquefaction, using a sophisticated constitutive model for the soil is indispensable. Such a model must adequately describe the material response to a cyclic loading under constant volume (undrained) conditions, amongst others the relaxation of effective stress (pore pressure accumulation) or the effective stress loops repeatedly passed through after a sufficiently large number of cycles (cyclic mobility, stress attractors). The soil behaviour under undrained cyclic loading is manifold, depending on the initial conditions (e.g. density, fabric, effective mean pressure, stress ratio) and the load characteristics (e.g. amplitude of the cycles, application of stress or strain cycles). In order to develop, calibrate and verify a constitutive model with focus to undrained cyclic loading, the data from high-quality laboratory tests comprising a variety of initial conditions and load characteristics are necessary. The purpose of these two companion papers was to provide such database collected for a fine sand. The database consists of numerous undrained cyclic triaxial tests with stress or strain cycles applied to samples consolidated isotropically or anisotropically. Monotonic triaxial tests with drained or undrained conditions have also been performed. Furthermore, drained triaxial, oedometric or isotropic compression tests with several un- and reloading cycles are presented. Part I concentrates on the triaxial tests with monotonic loading or stress cycles. All test data presented herein will be available from the homepage of the first author. As an example of the examination of an existing constitutive model, the experimental data are compared to element test simulations using hypoplasticity with intergranular strain.     

Shearing characteristics of SCP-inserted clay specimens in triaxial compression test

Sand compaction piles (SCPs) have been widely applied to the construction on the soft ground for decades, due to not only the acceleration of the consolidation but also the enhancement of strength and stiffness of ground. However, physical behaviors of SCP-improved ground have not been clearly unveiled due to complex response of two distinct materials, compacted sand and soft clay, which are having quite different mechanical characteristics. Therefore, in this study, the mechanical characteristics of SCP composite ground were investigated via triaxial compression tests on SCP-inserted clay specimens. Tests were performed elaborately with four specimens with different replacement ratios. Based on the comparisons of consolidation and shearing behaviors of tested SCP-inserted clay specimens, the SCP effects on the stiffness and strength are also investigated. Even though the SCP-inserted clay specimens show stronger and stiffer behaviors than clay-only specimens, the effects vary on strength, stiffness, and volume change with regard to the applied replacement ratios.     

Sand eddies induced by cyclic tilt of a retaining wall

The cyclic tilt of a retaining wall induces a peculiar motion in the backfill (sand), which exhibits closed trajectories (eddies). In this paper, the motion of the backfill has been optically traced and analyzed by means of particle image velocimetry, also known as digital image correlation. The results are of importance for cyclically loaded structures (e.g, piles for off-shore structures) and can also serve to test numerical simulations of large deformation.     

Effects of grain morphology on critical state: a computational analysis

We introduce a new DEM scheme (LS-DEM) that takes advantage of level sets to enable the inclusion of real grain shapes into a classical discrete element method. Then, LS-DEM is validated and calibrated with respect to real experimental results. Finally, we exploit part of LS-DEM potentiality by using it to study the dependency of critical state (CS) parameters such as critical state line (CSL) slope \(\lambda \), CSL intercept \(\varGamma \), and CS friction angle \(\varPhi _{\mathrm{CS}}\) on the grain’s morphology, i.e., sphericity, roundness, and regularity. This study is carried out in three steps. First, LS-DEM is used to capture and simulate the shape of five different two-dimensional cross sections of real grains, which have been previously classified according to the aforementioned morphological features. Second, the same LS-DEM simulations are carried out for idealized/simplified grains, which are morphologically equivalent to their real counterparts. Third, the results of real and idealized grains are compared, so the effect of “imperfections” on real particles is isolated. Finally, trends for the CS parameters (CSP) dependency on sphericity, roundness, and regularity are obtained as well as analyzed. The main observations and remarks connecting particle’s morphology, particle’s idealization, and CSP are summarized in a table that is attempted to help in keeping a general picture of the analysis, results, and corresponding implications.     

Impacts of mineralogical compositions on different trapping mechanisms during long-term CO<Subscript>2</Subscript> storage in deep saline aquifers

Deep saline aquifers in sedimentary basins are considered to have the greatest potential for CO₂ geological storage in order to reduce carbon emissions. CO₂ injected into a saline sandstone aquifer tends to migrate upwards toward the caprock because the density of the supercritical CO₂ phase is lower than that of formation water. The accumulated CO₂ in the upper portions of the reservoir gradually dissolves into brine, lowers pH and changes the aqueous complexation, whereby induces mineral alteration. In turn, the mineralogical composition could impose significant effects on the evolution of solution, further on the mineralized CO₂. The high density of aqueous phase will then move downward due to gravity, give rise to “convective mixing,” which facilitate the transformation of CO₂ from the supercritical phase to the aqueous phase and then to the solid phase. In order to determine the impacts of mineralogical compositions on trapping amounts in different mechanisms for CO₂ geological storage, a 2D radial model was developed. The mineralogical composition for the base case was taken from a deep saline formation of the Ordos Basin, China. Three additional models with varying mineralogical compositions were carried out. Results indicate that the mineralogical composition had very obvious effects on different CO₂ trapping mechanisms. Specific to our cases, the dissolution of chlorite provided Mg²⁺ and Fe²⁺ for the formation of secondary carbonate minerals (ankerite, siderite and magnesite). When chlorite was absent in the saline aquifer, the dominant secondary carbon sequestration mineral was dawsonite, and the amount of CO₂ mineral trapping increased with an increase in the concentration of chlorite. After 3000 years, 69.08, 76.93, 83.52 and 87.24 % of the injected CO₂ can be trapped in the solid (mineral) phase, 16.05, 11.86, 8.82 and 6.99 % in the aqueous phase, and 14.87, 11.21, 7.66 and 5.77 % in the gas phase for Case 1 through 4, respectively.     

Tailings composition effects on shear strength behavior of co-mixed mine waste rock and tailings

The objective of this study was to evaluate the effect of mine tailings composition on shear behavior and shear strength of co-mixed mine waste rock and tailings (WR&T). Crushed gravel was used as a synthetic waste rock and mixed with four types of tailings: (1) fine-grained garnet, (2) coarse-grained garnet, (3) copper, and (4) soda ash. Co-mixed WR&T specimens were prepared to target mixture ratios of mass of waste rock to mass of tailings (R) such that tailings “just filled” interparticle void space of the waste rock (i.e., optimum mixture ratio, R _opt). Triaxial compression tests were conducted on waste rock, tailings, and mixed waste at effective confining stresses (\(\sigma_{\text{c}}^{{\prime }}\)) ranging from 5 to 40 kPa to represent stresses anticipated in final earthen covers for waste containment facilities. Waste rock and co-mixed WR&T specimens were 150 mm in diameter by 300 mm tall, whereas tailings specimens were 38 mm in diameter by 76 mm tall. Shear strength was quantified using effective stress friction angles (?′) from undrained tests: ?′ for waste rock was 37°, ?′ for tailings ranged from 34° to 41°, and ?′ for WR&T mixtures ranged from 38° to 40°. Thus, shear strength of co-mixed WR&T was comparable to waste rock regardless of tailings composition. Shear behavior of WR&T mixtures was a function of R and tailings composition. Tailings influenced shear behavior for R < R _opt and when tailings predominantly were silt. Shear behavior was influenced by waste rock for R ≥ R _opt and when tailings predominantly were sand or included clay particles.