Double Strain Softening and Diagonally Crossing Shear Bands of Sand in Drained Triaxial Tests

A comprehensive understanding of the shear behavior of sand in the context of shear band development has not been achieved yet in spite of many detailed research works on each specified subject. In order to observe the entire drained shear behavior of Toyoura sand from the macromechanical point of view, conventional triaxial tests were performed and analyzed up to an axial strain of 30% for various void ratios, initial confining stresses, and stress paths, paying particular attention to volume changes. The strong correlation was found between “double strain softening” and “diagonally crossing shear bands” as a remarkable result. Finally, a qualitative explanation of relations among the stress–strain curve, the failure shape, the dilatancy index–strain curve and the strain localization, could be clearly made. Also, it is concluded that the dilatancy index is an indicator not only of the ratio of the volumetric strain increment to the axial strain increment but also the condition of the strain localization.     

Instability Conditions of Loose Sand in Plane Strain

When a loose sand specimen is loaded under an undrained condition, it may become unstable. The instability conditions may be specified by an instability line determined using undrained tests. However, the instability behavior of sand has seldom been studied under plane-strain conditions. Experimental data obtained under both triaxial and plane-strain conditions are presented in this paper to define the instability conditions of loose sand under plane-strain conditions. Using the state parameter, a unified relationship can be established between the normalized slope of instability line and the state parameters for both axisymmetric and plane-strain conditions. Using this relationship, the instability conditions established under axisymmetric conditions can also be used for plane-strain conditions.     

Instability and Static Liquefaction on Proportional Strain Paths for Sand at Low Stresses

The behavior of Hostun RF sand on proportional strain paths at low confining pressures (20 to 100 kPa) is considered in this paper. In such paths, a constant dilation rate is imposed during shear. The usual features of pore pressure increase (contracting material) or decrease (dilating material) are here observed depending upon whether the imposed dilation rate is respectively greater or smaller than the “natural” dilation rate at failure (as measured in a drained test). Particular attention is given to the static liquefaction phenomenon, which is seen to occur for loose as well as dense sand provided the imposed dilation rate is large enough to lead to a continuous pore pressure increase during shear. Instability tests performed at low confining pressures on proportional strain paths show that the instability line is strain path dependent. It does not coincide with the peak deviator stress line in proportional strain paths tests, in general, but does coincide with the line d2W = 0 (nil second increment of total work).     

Micromechanical Analysis for Interparticle and Assembly Instability of Sand

Instability of granular material may lead to catastrophic events such as the gross collapse of earth structures, and thus it is an important topic in geotechnical engineering. In this paper, we adopt the micromechanics approach for constitutive modeling, in which the soil is considered an assembly of particles, and the stress-strain relationship for the assembly is determined by integrating the behavior of the interparticle contacts in all orientations. Although analyses regarding material instability have been extensively studied for a soil element at the constitutive level, it has not been considered at the interparticle contact level. Through an eigenvalue analysis, two modes of instability are identified at the local contact level: the singularity of tangential stiffness matrix and the loss of positiveness of second-order work. The constitutive model is applied to simulate drained and undrained triaxial tests on Toyoura sand of various densities under various confining pressures. The predictions are compared with experimentally measured instability at the assembly level. The modes of stability at the interparticle contact level and their relations to the overall instability of the assembly are also analyzed.     

Undrained Anisotropic Monotonic Behavior of Sand from In Situ Tests

A procedure for estimating the undrained stress-strain behavior of sand from drained self-boring pressuremeter and seismic piezocone penetration tests is proposed in this paper. The procedure offers an inexpensive alternative to laboratory testing and avoids the uncertainty of the empirical methods based on index measurements such as the Standard Penetration Test blow count and the tip resistance in a Piezocone Penetration Test (CPTU). To check its validity, the proposed procedure was used to infer the undrained triaxial stress-strain curves and the results were compared with laboratory triaxial tests on undisturbed samples. The undrained limit equilibrium stability of a dike was also assessed using the inferred stress-strain behavior to illustrate the usefulness of the procedure. The result of the stability analysis was found to be in qualitative agreement with the observed performance of the dike during a recent field experiment attempting to trigger static liquefaction.     

Nonlocal Multilaminate Model for Strain Softening Analysis

A constitutive model formulated within the multilaminate framework is described in this paper. The basic model, incorporating deviatoric and volumetric hardening, was developed for normally consolidated or slightly overconsolidated clay. This model has been extended to account for shear softening by using a nonlocal formulation. The nonlocal plasticity is based on weighted average of plastic strains taken from neighboring material points within a certain distance which is a function of an internal length parameter. This parameter is related to the mean grain size that restricts the element size. By using a softening scaling this restriction can be eliminated and the model is therefore capable of simulating geotechnical boundary value problems. The capability of the model for simulating strain softening behavior is shown by numerical simulation of biaxial tests. Finally, the ground response curve obtained from the proposed model for excavation of a tunnel in soil is discussed.     

Strain Localization in Sand: Plane Strain versus Triaxial Compression

A comprehensive experimental investigation was conducted to investigate the effects of loading condition and confining pressure on strength properties and localization phenomena in sands. A uniform subrounded to rounded natural silica sand known as F-75 Ottawa sand was used in the investigation. The results of a series on conventional triaxial compression (CTC) experiments tested under very low-confining pressures (0.05–1.30) kPa tested in a microgravity environment abroad the NASA Space Shuttle are presented in addition to the results of similar specimens tested in terrestrial laboratory to investigate the effect of confining pressure on the constitutive behavior of sands. The behavior of the CTC experiments is compared with the results of plane strain experiments. Computed tomography and other digital imaging techniques were used to study the development and evolution of shear bands.     

Principal Deviatoric Strain Increment Ratios for Sand Having Inherent Transverse Isotropy

The behavior of sand on the π plane, including the relation between the principal deviatoric strain increment ratios, is not fully understood. The objectives are: To clarify experimentally the relation between the principal deviatoric strain increment ratios for sand in a wide range of b values and to discuss the basic shear behavior, taking particular notice of inherent transverse isotropy and noncoaxiality. From the experimental results on sand with inherent transverse isotropy, it was observed that the relation between the principal deviatoric strain increment ratios is fundamental and is related to the shape of the failure surface and the extent of strain localization. A new equation for the principal deviatoric strain increment ratios is proposed to model the influence of the incremental stress.     

State Pressure Index for Modeling Sand Behavior

The effort to model sand behavior within the framework of critical-state soil mechanics would benefit from a state variable that relates the current void ratio and mean pressure of the soil to its void ratio and mean pressure at the critical state. In this paper we propose a state pressure index, Ip, which is defined as the ratio of the current mean pressure to the mean pressure at the critical state that corresponds to the current void ratio. Using this state pressure index, a bounding surface hypoplasticity model for sand is modified so that the phase transformation and failure stress ratios both depend on Ip and merge into the critical-state stress ratio at failure. The Ip dependency introduced enables use of a single set of model constants in modeling sand behavior for various initial confining pressures and densities under both undrained and drained conditions. Dilatancy, strain softening, and strain hardening are simulated for both loose and dense sands. Simulations from the modified model are compared with results of laboratory tests of drained and undrained triaxial compression.     

再结晶软化程度对C-Mn钢变形抗力的影响

利用带钢热连轧的实测条件研究了再结晶软化程度对C-Mn钢变形抗力的影响。结果表明，根据金属的再结晶规律得到的实质应变，比计算“残留应变率”法不但与实测更为接近，而且更符合理论结果；考虑再结晶软化程度对变形抗力的影响后使轧机负荷的预报精度得到明显提高；给出的C-Mn钢静态再结晶模型所得结果与实测符合得较好，从而为控制产品的组织性能提供了奥氏体再结晶的定量化依据。     

Mesh Dependence and Nonlocal Regularization of One-Dimensional Strain Softening Plasticity

Finite-element analysis of strain localization based on classical theory of continuum mechanics suffers from pathological mesh dependence when strain softening models are used. For quasistatic problems, the mesh dependence is demonstrated through an analysis of the tangent stiffness matrix of a one-dimensional problem. To regularize the mesh dependence, a nonlocal strain softening model is proposed, which is based on the nonlocal plasticity theory and the representative line element. Both analytical and numerical solutions of strain localization with the proposed model are developed and compared with each other. The model is also applied in the numerical simulation of a direct tensile test of a concrete specimen in the existing literature, and reasonable agreement is achieved between numerical solutions and the experimental response.     

Modeling the Stress-Strain Relations of Sand in Cyclic Plane Strain Loading

A modeling procedure to simulate stress-strain relations of sand subjected to cyclic loading is proposed. Results from drained plane strain compression, extension, and cyclic loading tests on Toyoura sand are analyzed. The monotonic loading behavior is simulated by the generalized hyperbolic equation to use as the skeleton curves in the simulation of cyclic behavior. To construct hysteretic stress-strain curves based on the skeleton curves, the Masing’s rule is generalized to the proportional rule consisting of the internal and external rules. The drag rule is then introduced to simulate cyclic stress-strain behavior in which the stress amplitude increases at a decreasing rate during cyclic loading with a constant strain amplitude. It is assumed that any plastic shear strain increment taking place in a certain direction drags the whole skeleton curve for loading in the opposite direction towards the direction of the concerned shear strain increment. The measured cyclic stress-strain behavior is well simulated by the proposed method.     

Shear Strength Behavior of Fiber-Reinforced Sand Considering Triaxial Tests under Distinct Stress Paths

The results of drained triaxial tests on fiber reinforced and nonreinforced sand (Osorio sand) specimens are presented in this work, considering effective stresses varying from 20 to 680?kPa and a variety of stress paths. The tests on nonreinforced samples yielded effective strength envelopes that were approximately linear and defined by a friction angle of 32.5° for the Osorio sand, with a cohesion intercept of zero. The failure envelope for sand when reinforced with fibers was distinctly nonlinear, with a well-defined kink point, so that it could be approximated by a bilinear envelope. The failure envelope of the fiber-reinforced sand was found to be independent of the stress path followed by the triaxial tests. The strength parameters for the lower-pressure part of the failure envelope, where failure is governed by both fiber stretching and slippage, were, respectively, a cohesion intercept of about 15?kPa and friction angle of 48.6?deg. The higher-pressure part of the failure envelope, governed by tensile yielding or stretching of the fibers, had a cohesion intercept of 124?kPa, and friction angle of 34.6?deg. No fiber breakage was measured and only fiber extension was observed. It is, therefore, believed that the fibers did not break because they are highly extensible, with a fiber strain at failure of 80%, and the necessary strain to cause fiber breakage was not reached under triaxial conditions at these stress and strain levels.     

Strain Rate, Creep, and Stress Drop-Creep Experiments on Crushed Coral Sand

The part of sand behavior that is affected by time, such as creep, relaxation, and loading rate effects are not similar to those observed for clay. To throw more light on the time effects in sand, many series of drained triaxial compression experiments have been performed on crushed coral sand. These tests were all performed with a constant effective confining pressure of 200?kPa. The test series included experiments with specimens loaded at five different strain rates with a 256-fold ratio between the extreme rates, tests with sudden changes in strain rate from slow to fast and vice versa, and tests in which axial and volumetric creep strains were observed at stress differences of 500, 700, and 900?kPa. Creep creates structuration and this has to be overcome to produce further plastic straining. Experiments were also performed in which the stress difference was dropped quickly from three different values of 500, 700, and 900?kPa followed by creep. In these stress drop-creep tests five different magnitudes of stress drops were employed: 0, 100, 200, 300, and 400?kPa. The results involving conventional creep effects and stress drop-creep effects are presented and analyzed.     

Behavior of Step Tapered Bored Piles in Sand under Static Lateral Loading

The behavior of step tapered bored piles in sand, under static lateral loading, was examined by field tests at one site in Kuwait. A total of 14 bored piles including two instrumented piles were installed for lateral loading. The soil profile consists of medium dense sand with weak cementations and no groundwater was encountered in the boreholes. Laboratory tests were carried out to determine the basic soil characteristics and the strength parameters. Both the ultimate lateral capacity and the deflections at applied loads were examined. The results indicate increased lateral load carrying capacity and decreased deflections at different applied loads for the step tapered piles due to the enlargement or strengthening of the upper section of the piles. The advantages of using this type of pile is emphasized including the cost saving resulting from an economical design.     

Behavior of Model Rafts Resting on Pile-Reinforced Sand

Piles in a pile raft are sometimes considered as settlement reducers, not load-carrying members. In design, one often tries to minimize the number of piles. This often results in a high axial stress in the piles that may deter their use due to the limits on pile stress in practice. An alternative is to consider the pile as reinforcement in the base soil, and not as a structural member. Serving as a soil stiffener, the pile can tolerate a lower safety margin against structural failure without violating building codes. Previous numerical studies on the use of disconnected piles as settlement reducers have shown the effectiveness of such piles. This study aims to verify experimentally the effectiveness of such piles through load tests of model rafts resting on pile-reinforced sand. By varying factors such as raft stiffness, pile length, pile arrangement, and pile number, results of the investigation indicate that structurally disconnected piles are effective in reducing the settlement and bending moments in the model rafts.     

Characterization of Fines Produced by Sand Crushing

Sand particle crushing generates coarse fragments with size d ≥ 75?μm and fine fragments, i.e., “fines,” with size d<75?μm. Yet, postcrushing fines are seldom characterized due to testing constraints. An experimental study was conducted to examine the size distribution evolution of fine fragments generated by crushing two uniform sands with contrasting degrees of mineral composition heterogeneity, in one-dimensional compression. The determination of fine fragment sizes was made possible by using a particle size analyzer that employs a small sample. The results indicate that the degree of mineral composition heterogeneity affects the load–deformation behavior of crushing sands and the resulting amounts and size distribution evolutions of the produced coarse and fine fragments. In particular, the trends gathered suggest that fines generation occurs by abrasion of parent particles, coarse fragment breakage, and subsequent breakage of fine fragments with sizes larger than the comminution limit.     

Saturation and Preloading Effects on the Cyclic Behavior of Sand

In order to study pore water pressure response and liquefaction characteristics of sand, which has previously experienced liquefaction, two series of cyclic triaxial tests were run on medium dense sand specimens. In the first test series the influence of the soil saturation under undrained cyclic loading has been studied. It summarizes results of cyclic triaxial tests performed on Hostun-RF sand at various values of the Skempton’s pore-pressure coefficient. Analysis of experimental results gives valuable insights on the effect of soil saturation on sand response to undrained cyclic paths. In the second series of tests, the preloading influence on the resistance to the sands liquefaction has been realized on samples at various histories of loading. It was found that a large preloading induces a reduction of the resistance of sands to liquefaction.     

Contraction, Dilation, and Failure of Sand in Triaxial, Torsional, and Rotational Shear Tests

The response of a saturated fine sand (Nevada sand No. 120) with relative density Dr ≈ 70% in drained and undrained conventional triaxial compression and extension tests and undrained cyclic shear tests in a hollow cylinder apparatus with rotation of the stress directions was studied. It was observed that the peak mobilized friction angle for this dilatant material was different in undrained and drained tests; the difference is attributed to the fact that the rate of dilation is smaller in an undrained test than it is in a drained test. Consistent with the findings of others, the material is more resistant to undrained cyclic loading for triaxial compression than for triaxial extension. In rotational shear tests in which the second invariant of the deviatoric stress tensor is held constant, the shear stress path (after being normalized by the mean normal effective stress) approached an envelope that is comparable but not identical in shape to a Mohr-Coulomb failure surface. As the stress path approached the envelope, the shear end deviatoric strains continued to increase in an unsymmetrical smooth spiral path. During the rotational shear tests, the direction of the deviatoric strain-rate vector (deviatoric strain increment divided by the magnitude of change in Lode angle) was observed to be about midway between the deviatoric stress increment vector and the normal to a Mohr-Coulomb failure surface in the deviatoric plane. The stress ratio at the transition from contractive to dilative behavior (i.e., “phase transformation”) was also observed to depend on the direction of the stress path; therefore this stress ratio is not a fundamental property. Results from torsional hollow cylinder tests with rotation of stress directions are presented in new graphical formats to help understand and interpret the fundamental soil behavior.     

Interference of Two Closely Spaced Strip Footings on Sand Using Model Tests

By using small scale model tests, the interference effect on the ultimate bearing capacity of two closely spaced strip footings, placed on the surface of dry sand, was investigated. At any time, the footings were assumed to (1) carry exactly the same magnitude of load; and (2) settle to the same extent. No tilt of the footing was allowed. The effect of clear spacing (s) between two footings was explicitly studied. An interference of footings leads to a significant increase in their bearing capacity; the interference effect becomes even more substantial with an increase in the relative density of sand. The bearing capacity attains a peak magnitude at a certain (critical) spacing between two footings. The experimental observations presented in this technical note were similar to those given by different available theories. However, in a quantitative sense, the difference between the experiments and theories was seen to be still significant and it emphasizes the need of doing a further rigorous analysis in which the effect of stress level on the shear strength parameters of soil mass can be incorporated properly.