Effect of particle friction and polydispersity on the macroscopic stress–strain relations of granular materials

The macroscopic mechanical behavior of granular materials inherently depends on the properties of particles that compose them. Using the discrete element method, the effect of particle contact friction and polydispersity on the macroscopic stress response of 3D sphere packings is studied. The analytical expressions for the pressure, coordination number and fraction of rattlers proposed for isotropically deformed frictionless systems also hold when the interparticle coefficient of friction is finite; however, the numerical values of the parameters such as the jamming volume fraction change with varying microscopic contact and particle properties. The macroscopic response under deviatoric loading is studied with triaxial test simulations. Concerning the shear strength, our results agree with previous studies showing that the deviatoric stress ratio increases with particle coefficient of friction μ starting from a nonzero value for μ = 0 and saturating for large μ. On the other hand, the volumetric strain does not have a monotonic dependence on the particle contact friction. Most notably, maximum compaction is reached at an intermediate value of the coefficient of friction μ ≈ 0.3. The effect of polydispersity on the macroscopic stress–strain relationship cannot be studied independent of initial packing conditions. The shear strength increases with polydispersity when the initial volume fraction is fixed, but the effect of polydispersity is much less pronounced when the initial pressure of the packings is fixed. Finally, a simple hypoplastic constitutive model is calibrated with numerical test results following an established procedure to ascertain the relation between particle properties and material coefficients of the macroscopic model. The calibrated model is in good qualitative agreement with simulation results.     

Nonlinear analysis of footings on granular bed–stone column improved soft soil

In this paper, a model for the analysis of footings having finite flexural rigidity resting on a granular bed on top of stone columns improved saturated soft (clayey) soil has been proposed. Soft soil has been modeled as a Kelvin–Voigt body to represent its time dependent behavior. Pasternak shear layer has been used to represent the granular layer and the stone columns have been idealized by means of nonlinear Winkler springs. Nonlinear behavior of granular fill, soft soil and stone columns has been invoked by means of hyperbolic constitutive relationships. Governing differential equations for the soil–foundation system have been obtained and finite difference method has been adopted for solving these, using the Gauss-elimination iterative scheme. Detailed parametric study for a combined footing has been carried out to study the influence of parameters, like magnitude of applied load, flexural rigidity of footing, diameter of stone column, spacing of stone column, ultimate bearing capacity of granular fill, poor foundation soil and stone column, relative stiffness of stone columns and degree of consolidation, on flexural response of the footing.     

Comprehensive laboratory study on stress–strain of granular soils at constant global void ratio: combined effects of fabrics and silt content

The published literature has revealed conflicting results regarding the effect of low plastic fines fraction (I_p?≤?5.0%) on the mechanical behavior of sandy soils. For this reason, the use of different sample initial structures as (initial relative density approach, global void ratio index approach, etc.) could explain these different mechanical responses of granular materials. Thus, it is necessary to evaluate the quantitative aspect of the low plastic fines effects on the undrained monotonic response of sand-silt mixtures using the global void ratio approach. To achieve this goal, an experimental testing program through controlled monotonic triaxial tests was carried out on reconstituted saturated Chlef sand containing from 0 to 50% silt with an interval of 10% at three global void ratios (e?=?0.64, 0.66 and 0.68) and subjected to constant confining pressure (σ'₃?=?100 kPa). The different samples were reconstituted using two different preparation techniques: DFP and MT. The obtained results show that the low plastic fines content appears as a very relevant parameter in the characterization of the mechanical response of sand-silt mixture samples reconstituted at constant global void ratios, where the steady state shear strength and instability shear strength decreased with the increase in low plastic fines content up to the limiting fines contents (F_c?=?40% and F_c?=?10%) considering both studied initial structures (Dry funnel pluviation and Moist tamping), respectively. Beyond these thresholds fines contents, a reverse trend was observed for all parameters under study. Moreover, the test results indicate that the brittleness index, flow potential (V_f), friction index, equivalent void ratio (e*) and equivalent relative density (Dr*) could be considered as reliable parameters in the prediction of the mechanical behavior of the silty sand soils under study.

     

Intelligent prediction of the stress–strain response of intact and jointed rocks

An application of Artificial Neural Networks for predicting the stress–strain response of jointed rocks under different confining pressures is presented in this paper. Rocks of different compressive strength with different joint properties (frequency, orientation and strength of joints) are considered in this study. The database for training the neural network is formed from the results of triaxial compression tests on different intact and jointed rocks with different joint properties tested at different confining pressures reported by various researchers in the literature. The network was trained using a three-layered network with the feed-forward back propagation algorithm. About 85% of the data was used for training and the remaining 15% was used for testing the network. Results from the analyses demonstrated that the neural network approach is effective in capturing the stress–strain behaviour of intact rocks and the complex stress–strain behaviour of jointed rocks. A single neural network is demonstrated to be capable of predicting the stress–strain response of different jointed rocks, whose intact strength varies from 11.32 MPa to 123 MPa, spacing of joints varies from 10 cm to 100 cm, and confining pressures range from 0 to 13.8 MPa.     

Stress ratio–fabric relationships of granular soils under axi-symmetric stress and plane-strain loading

This paper investigates the relationship between the stress ratio and the fabric of frictional material under three-dimensional stress. The spatial distribution function of the contact normal was derived to describe the heterogeneous distribution of the micro-structural architecture. Discrete element simulations were conducted using an assembly consisting of 10,000 spherical particles. Sixteen stress probe experiments were simulated under both axi-symmetric stress and plane-strain conditions. The numerical results show that a change in the direction of the stress probe does not significantly affect the evolution of the fabric structure in the vertical plane. Regardless of whether the material is subjected to axi-symmetric stress or plane strain, the degree of fabric anisotropy shows a unique relationship with the stress ratio. The modified stress ratio, as theoretically derived from a micromechanics formulation, is able to separately measure micro-structures in the vertical and horizontal planes. The distribution function proposed in this study generally performs well in estimating the heterogeneous distribution of the contact normal. A higher-order distribution function is required to improve the predictability of the contact normal distribution for increasing stress-ratio paths.     

Geodynamics and stress–strain patterns in different tectonic settings

Deformation patterns in subduction zones, feeder systems of volcanoes, and rifts are compared and investigated in terms of relations among elastoplastic strain, rheology, pore fluids, and temperature. Regional-scale subduction processes have been explored in segments of the Kuriles–Kamchatka, Izu-Bonin, and Mariana zones. Slab geometry constraints from the 3D velocity structure are used to model the balance of forces in the three subduction zones and to distinguish the regions of predominant push or pull. Stress and strain variations in suprasubduction crust are considered for the case of magma sources beneath the Klyuchevskoy group of volcanoes. Time-lapse (4D) seismic tomography shows crustal magma reservoirs to appear and disappear rapidly as the volcanoes become active or dormant, respectively. This behavior is due to rapid strain changes which cause fast flow of fluids and the ensuing decrease or increase of melting temperature in the magma reservoirs. In addition to subduction zones, stress–strain patterns are modeled for collisional (compressive) settings, with the example of the Altai–Sayan area and the Caucasus, and for the conditions of rifting (extension), in the case of the Vilyui basin. As the modeling shows, formation of a superdeep basin does not necessarily require the crust to stretch twice or more: only 20% stretching in the necking region is enough to produce a 10–15 km deep basin.     

The future of failure: stress or strain?

Strains in rocks can be observed but ancient stresses can only be inferred. We should re-examine the potential of strain geometry as the key to understanding and interpreting common shear structures ranging from faults to plastic shear zones. The concept of failure along zero extension directions can be applied to natural structures in rocks and is predicated on strain compatibility between differently strained volumes. Zero extension directions are considered for two strain configurations, plane strain (k=1) and uniaxial shortening (k=0). The crucial difference between shear fractures, or faults, and plastic yield zones is that the former are preceded by dilatation while the latter are isovolumetric. Volume changes during deformation affect the orientations of zero extension directions and hence of the resulting structures. With isovolumetric strain, yield occurs on planes at 45° to the principal shortening direction in plane strain and at 54.7° to this axis in uniaxial shortening. Uniaxial shortening experiments on rock samples allow estimation of the relative volumetric strains when yield zones initiate. When this volumetric strain is used to estimate the orientation of shear fractures in plane strain, ca 70° dips are predicted for normal faults at high crustal levels, decreasing downwards to 45°.     

Effect of microstructure on stress–strain and pore-pressure response of sabarmati sand under the influence of mica

ABSTRACT

Micaceous soil is believed to be detrimental for civil engineering constructions due to the effect of high compressibility, low compacted density and low shear strength. Individual mica particle has numerous intact mica flakes foliated over each other making it flexible upon loading and rebound upon unloading due to its low hardness and resilient nature. Hence, micaceous soils with mica content more than 10% are considered undesirable for highway pavements, embankments and railway track constructions. When platy mica particles are sufficiently numerous to interact with spherical sand particles, bridging and ordering phenomena are augmented within the soil mass creating unique sand-mica particle orientation (MS microstructure) unlike sand-sand particle orientation (PS microstructure). The current experimental research was conducted to evaluate the variation in stress–strain, pore pressure and effective stress path response of Sabarmati sand under the influence of mica (sand with 30% mica and pure sand) with MS and PS microstructure respectively. Effect of particle crushing on stress–strain and pore pressure response was also studied on Sabarmati sand with MS and PS microstructure. Distinctive macroscopic response was observed in Sabarmati sand with MS microstructure under the influence of mica as well as mica particle crushing.     

Hybrid continuum–discrete simulation of granular impact dynamics

Acta Geotechnica - Granular impact—the dynamic intrusion of solid objects into granular media—is widespread across scientific and engineering applications including geotechnics....     

Consolidation behavior of soil–cement column improved ground

Columnar inclusion is one of the effective and widely used methods for improving the engineering properties of soft clay ground. This article investigates the consolidation behavior of composite soft clay ground using both physical model tests under an axial-symmetry condition and finite element simulations using the PLAXIS 2D program. It was determined that the final settlement and the rate of consolidation of the composite ground depended on the stress state. For an applied stress that is much lower than the failure stress, the final settlement of the composite ground was lower, and the consolidation was rapid. When the soil–cement column failed, the stress on the column suddenly decreased (due to strain-softening); meanwhile, the stress on the soil increased to maintain the force equilibrium. Consequently, the excess pore pressure in the surrounding clay increased immediately. The cracked soil–cement column acted as a drain, which accelerated the dissipation of the excess pore pressure. The consolidation of the composite ground was mainly observed in the vertical direction and was controlled by the area ratio, which is the ratio of the diameter of the soil–cement column to the diameter of the composite ground, a. The stress on the column was shown to be low for a composite ground with a high value of a, which resulted in less settlement and fast consolidation. For a long soil–cement column, the excess pore pressures in the surrounding clay and the column were essentially the same at a given consolidation time throughout the improvement depth. It is proposed that the soil–cement column and surrounding clay form a compressible ground, and the consolidation occurs in the vertical direction. The composite coefficient of consolidation (c_v(com₎) that was obtained from the physical model test on the composite ground can be used to approximate the rate of consolidation. This approximation was validated via a finite element simulation. The proposed method is highly useful to geotechnical engineers because of its simplicity and reliable prediction.     

Why the OCR may reduce the small strain shear stiffness of granular materials?

The small strain shear stiffness G₀ of the soil is of interest and importance in both theory and practice. It is expected that for granular materials G₀ would slightly increases with over-consolidation ratio (OCR). However, laboratory tests indicate that G₀ may decrease with increasing OCR, especially for loose specimens, which is counterintuitive. To explore the underlying mechanism, discrete element method (DEM) is used to investigate the effect of OCR on G₀. The DEM simulations successfully capture the laboratory observations. The analyses at the particulate level reveal that the decrease in small strain stiffness is mainly due to the decreases in coordination number and the uniformity of contact force distribution during unloading process.     

Three-dimensional DEM modeling of the stress–strain behavior for the gap-graded soils subjected to internal erosion

In this work, 3D discrete element method modeling of drained shearing tests with gap-graded soils after internal erosion is carried out based on published experimental results. The erosion in the model is achieved by randomly deleting fine particles, mimicking the salt dissolving process in the experiments. The present model successfully simulates the stress–strain behavior of the physical test by employing the roll resistance and lateral membrane. The case without erosion shows a strain-softening and dilative response, while strain-hardening and contractive response starts to occur as the degree of erosion increases. The dilative to contractive transition is mainly caused by the increase in void ratio due to the loss of fine particles. The change from dilative behavior to contractive behavior is more abrupt for the specimen with larger fine particle percentage because the soil skeleton is mainly controlled by the fine particles instead of by the coarse soil particles. The transition from “fines in sand” to “sand in fines” might be associated with the rapid increasing in the contacts associated with fine particles in the specimen as the percentage of fine content increases. The erosion scenario based on the hydraulic gradient is also modeled by deleting the fine particles based on the ranking of the contact force. Compared with the scenario based on random deletion, the remaining fine particles for the erosion scenario based on the ranking of contact force are more dispersedly distributed, which might benefit the small strain stiffness but result in a smaller strength. This work provides some insights for better understanding the mechanism behind the internal erosion and the associated stress–strain behavior of soil. The gradient of the critical state line increases with more loss of fine particles denoting that the fine particles are helpful for holding the structure of the soils from larger deformation.

     

Collapse of granular–cohesive soil mixtures on a horizontal plane

Acta Geotechnica - The collapse test with granular or cohesive materials known as ‘slump test’ is a simple, small-scale experiment. It can be used to study the rheology of soil masses...     

Young,active conjugate strike–slip deformation in West Sichuan: evidence for the stress–strain pattern of the southeastern Tibetan Plateau

The active kinematics of the eastern Tibetan Plateau are characterized by the southeastward movement of a major tectonic unit, the Chuan-Dian crustal fragment, bounded by the left-lateral Xianshuihe–Xiaojiang fault in the northeast and the right-lateral Red River–Ailao Shan shear zone in the southwest. Our field structural and geomorphic observations define two sets of young, active strike–slip faults within the northern part of the fragment that lie within the SE Tibetan Plateau. One set trends NE–SW with right-lateral displacement and includes the Jiulong, Batang, and Derong faults. The second set trends NW–SE with left-lateral displacement and includes the Xianshuihe, Litang, Xiangcheng, Zhongdian, and Xuebo faults. Strike–slip displacements along these faults were established by the deflection and offset of streams and various lithologic units; these offsets yield an average magnitude of right- and left-lateral displacements of ～15–35 km. Using 5.7–3.5 Ma as the time of onset of the late-stage evolution of the Xianshuihe fault and the regional stream incision within this part of the plateau as a proxy for the initiation age of conjugate strike–slip faulting, we have determined an average slip rate of ～2.6–9.4 mm/year. These two sets of strike–slip faults intersect at an obtuse angle that ranges from 100° to 140° facing east and west; the fault sets define a conjugate strike–slip pattern that expresses internal E–W shortening in the northern part of the Chuan-Dian crustal fragment. These conjugate faults are interpreted to have experienced clockwise and counterclockwise rotations of up to 20°. The presence of this conjugate fault system demonstrates that this part of the Tibetan Plateau is undergoing not only southward movement, but also E–W shortening and N–S lengthening due to convergence between the Sichuan Basin and the eastern Himalayan syntaxis.     

Phenomenological fractional stress–dilatancy model for granular soil and soil-structure interface under monotonic and cyclic loads

The stress–dilatancy relation is of critical importance for constitutive modelling of geomaterial. A novel fractional-order stress–dilatancy equation had been developed for granular soil, where a nonlinear stress–dilatancy response was always predicted. However, it was experimentally observed that after a certain extent of shearing, an almost linear response between the stress ratio and the dilatancy ratio, rather than the nonlinear response, usually existed. To capture such stress–dilatancy behaviour, a new fractional stress–dilatancy model is developed in this study, where an apparent linear response of the stress–dilatancy behaviour of soil after sufficient shearing is obtained via analytical solution. As the fractional order varies, the derived stress–dilatancy curve and the associated phase transformation state stress ratio keep changing. But, unlike existing researches, no other specific parameters, except the parameter related to fractional order, concerning such shift are required. Then, the developed stress–dilatancy model is applied to constitutive modelling of granular soil and soil–structure interface, for further validation. A series of test results of different granular soils and soil–structure interfaces under different loading conditions are simulated and compared, where a good model performance is observed.

     

Enhancement of a hypoplastic model for granular soil–structure interface behaviour

Modelling of interfaces in geotechnical engineering is an important issue. Interfaces between structural elements (e.g., anchors, piles, tunnel linings) and soils are widely used in geotechnical engineering. The objective of this article is to propose an enhanced hypoplastic interface model that incorporates the in-plane stresses at the interface. To this aim, we develop a general approach to convert the existing hypoplastic model with a predefined limit state surface for sands into an interface model. This is achieved by adopting reduced stress and stretching vectors and redefining tensorial operations which can be used in the existing continuum model with few modifications. The enhanced interface model and the previous model are compared under constant-load, stiffness and volume conditions. The comparison is followed by a verification of two the approaches for modelling the different surface roughness. Subsequently, a validation between available experimental data from the literature versus simulations is presented. The new enhanced model gives improved predictions by the incorporation of in-plane stresses into the model formulation.     

Recent structures and tectonic regimes of the stress–strain state of the Earth’s crust in the northeastern sector of the Russian Arctic region

A comprehensive investigation aimed at determining seismotectonic types of destruction and the stress–strain state of the Earth’s crust in the main seismogenerating structures of the Arctic–Asian seismic belt is conducted for the territory of the northeastern sector of the Russian Arctic region. Based on the degree of activity of geodynamical processes, the regional principles for ranking neotectonic structures are elaborated, and neotectonic zoning is carried out based on the substantiated differentiation of the corresponding classes. Within the limits of the Laptev Sea, Kharaulakh, and Lena-Anabar segments, we analyzed I the structural–tectonic position of the most recent structures, II the deep structure parameters, III the parameters of the active fault system, and IV the parameters of the tectonic stress field, as revealed from tectonophysical analysis of Late Cenozoic fault and fold deformations. Based on the seismological data, the mean seismotectonic deformation tensors are calculated to determine, in combination with geological and geophysical data, the orientations of the principal stress axes and to reveal the structural–tectonic regularity for tectonic regimes of the stress–strain state of the Earth’s crust in the Arctic sector of the boundary between the Eurasian and North American lithospheric plates.     

A Numerical–Analytical Approach to Modeling the Axial Rotation of the Earth

A model for the non-uniform axial rotation of the Earth is studied using a celestial-mechanical approach and numerical simulations. The application of an approximate model containing a small number of parameters to predict variations of the axial rotation velocity of the Earth over short time intervals is justified. This approximate model is obtained by averaging variable parameters that are subject to small variations due to non-stationarity of the perturbing factors. The model is verified and compared with predictions over a long time interval published by the International Earth Rotation and Reference Systems Service (IERS).     

Stress–strain behavior of cement-improved clays: testing and modeling

The results of a series of laboratory tests on unimproved and cement-improved specimens of two clays are presented, and the ability of a bounding surface elastoplastic constitutive model to predict the observed behavior is investigated. The results of the oedometer, triaxial compression, extension, and cyclic shear tests demonstrated that the unimproved soil behavior is similar to that of soft clays. Cement-improved specimens exhibited peak/residual behavior and dilation, as well as higher strength and stiffness over unimproved samples in triaxial compression. Two methods of accounting for the artificial overconsolidation effect created by cement improvement are detailed. The apparent preconsolidation pressure method is considerably easier to use, but the fitted OCR method gave better results over varied levels of confining stresses. While the bounding surface model predicted the monotonic behavior of unimproved soil very well, the predictions made for cyclic behavior and for improved soils were only of limited success.