Instability in Granular Materials: Experimental Evidence of Diffuse Mode of Failure for Loose Sands

The influence of three loading paths on the collapse of loose sand is analyzed with a particular attention paid to the onset of collapse and the mode of failure exhibited. Experimental results on conventional undrained triaxial compression tests, constant shear drained tests, as well as quasi-constant shear undrained path are presented, compared, and analyzed. It is now recognized that some collapses can occur before the Mohr-Coulomb plastic limit criterion is reached, and our recent results obtained with the new arrangement built up highlight that these collapses occur under a diffuse mode of failure. An extensive experimental series of tests shows that the first negative value of the second-order work computed using experimental data corresponds to the loss of controllability. Moreover, it is shown that the stress ratios at collapse and the corresponding mobilized angles of friction are very close for all types of tests. For similar void ratios, the onset of collapse is thus largely independent of the loading path under drained and undrained conditions but depends on a stress state to bring the material inside the unstable domain and also on the current direction of the stress increment. Indeed, it appears that the orientations of the stress increments at collapse for all tests are the same, what explains, according to the second-order work criterion, that collapse occurs at the same stress ratio. A potentially unstable domain, depending on the stress increment direction, can thus be defined.     

Use of = 0 as a Failure Criterion for Weakly Cemented Soils

There is considerable uncertainty in the determination of effective stress strength parameters of cemented soils from undrained triaxial tests. Large negative excess pore pressures are generated at relatively large strains (typically 4–5% for cemented silty sand) in isotropically consolidated undrained (CIU) tests, which results in gas coming out of solution during shear and significant variability in the measured peak deviator stress. In this study, different failure criteria for weakly cemented sands were evaluated based on the results of CIU and isotropically consolidated drained triaxial compression tests conducted on samples of artificially cemented sand. The use of = 0 as a failure criterion eliminates the variability between the undrained tests and also ensures that the mobilized failure strength is not based on the highly variable negative excess pore pressures. In addition, the resulting strains to failure are comparable to the strains to failure for the drained tests. Mohr-Coulomb strength parameters thus estimated from the undrained tests are generally lower than strength parameters obtained from drained tests, and the difference between the failure envelopes from undrained tests increases as the level of cementation increases. This divergence is attributed to differences in the stiffness of the cemented soil under the different loading conditions. The stiffness under undrained loading conditions decreases with increasing cementation due to an increase in the generation of positive excess pore pressure at low strains.     

Drained Deformation Behavior of Anisotropic Sands during Cyclic Rotation of Principal Stress Axes

A series of drained tests for sands with inherent fabric anisotropy were conducted with an automatic hollow cylinder apparatus. The samples were subjected to cyclic rotation of principal stress axes while the magnitudes of effective principal stresses were maintained constant. The evolution of strain components and the volumetric strain with number of cycles, the relationship between the shear stress and shear strain components, and the flow rule of sands were investigated. It is found that plastic deformation is induced due to principal stress axes’ rotation alone without variation in the magnitudes of effective principal stresses. The contractive volumetric strain accumulates steadily with the increasing number of cycles; however, its accumulation rate is lowered with its progressive accumulation. The results also exhibit obvious noncoaxiality between the directions of strain increment and stress, and the noncoaxiality shows segmentation characteristics during the rotation of principal stress axes. Meanwhile, special attention was paid to the significant role of the intermediate principal stress parameter b [b = (σ2′?σ3′)/(σ1′?σ3′)] in the deformation behavior of sands during cyclic rotation of principal stress axes. It is found that the volumetric strain and the shear modulus ratio of the jth cycle to the first cycle increase with the increase in the b value under otherwise identical conditions. The effects of the relative density, effective mean normal stress, and deviatoric stress ratio on sand deformation behavior are also addressed in this work.     

Yield, Strength, and Critical State Behavior of a Tropical Saturated Soil

The paper reports laboratory investigations carried out on a tropical soil profile to study its compressibility, strength, critical state and limit state conditions, and their variation with depth. The soil profile comprises a reddish lateritic layer (horizon B) underlain by a saprolitic soil (horizon C) from which a number of block samples were taken. A series of isotropic and anisotropic compression tests, and drained and undrained triaxial tests, were conducted on specimens sampled at depths between 1.0 and 7.0 m, and also in the exposed saprolitic soil. Special triaxial tests, with the pore pressure increased to induce failure, were performed to investigate the failure at low stress levels. On this basis a tensile cutoff on the failure envelope was defined. In order to assess the influence of the natural soil structure, drained and undrained triaxial tests were carried out on compacted samples obtained from depths of 1.0 and 5.0 m. Higher strength parameters were measured for the horizon C soil, which is consistent with its lower clay content. A nonlinearity in the critical state line in q:p′ stress space was identified, but linear regression was used to obtain critical state parameters. The limit state curves for soils from horizon B are centered on the hydrostatic axis, but limit state curves for horizon C suggested anisotropic behavior.     

Liquefaction and Undrained Response Evaluation of Sands from Drained Formulation

A general approach has been established to assess the undrained stress-strain curve and effective stress path under monotonic loading from drained triaxial tests. An appropriate formulation of a drained and drained rebounded (i.e., overconsolidated) triaxial test response is developed that, in turn, allows the assessment of developing liquefaction and the undrained behavior of saturated sands. The formulation presented is based upon reported experimental drained test results that were obtained from different investigators using different testing techniques. This formulation is a function of the confining pressure and basic properties of the sand, such as relative density, uniformity coefficient, and particle shape (roundness), which can be obtained from visual inspection. The approach is verified by comparing predicted and reported (observed) undrained behavior. The developed formulas allow one to predict the potential of sand to liquefy, the type of liquefaction, the peak and residual strength values, as well as the whole undrained stress-strain curve and effective stress path. The simplicity of this approach makes it an attractive general method to characterize the undrained behavior of sands in a preliminary analysis with no need to run sophisticated experimental tests.     

Shear Strength and Pore-Water Pressure Characteristics during Constant Water Content Triaxial Tests

Shear strength parameters used in geotechnical design are obtained mainly from the consolidated drained (CD) or consolidated undrained (CU) triaxial tests. However in many field situations, soils are compacted for construction purposes and may not follow the stress paths in CD or CU triaxial tests. In these cases, the excess pore-air pressure during compaction will dissipate instantaneously, but the excess pore-water pressure will dissipate with time. Under this condition, it can be considered that the air phase is drained and the water phase is undrained. This condition can be simulated in a constant water content (CW) triaxial test. The purpose of this paper is to present the characteristics of the shear strength, volume change, and pore-water pressure of a compacted silt during shearing under the constant water content condition. A series of CW triaxial tests was carried out on statically compacted silt specimens. The experimental results showed that initial matric suction and net confining stress play an important role in affecting the characteristics of the shear strength, pore-water pressure, and volume change of a compacted soil during shearing under the constant water content condition. The failure envelope of the compacted silt exhibited nonlinearity with respect to matric suction.     

Modeling Cross Anisotropy in Granular Materials

A constitutive model has been developed to capture the behavior of cross-anisotropic frictional materials. The elastoplastic, single hardening model for isotropic materials serves as the basic framework. Based on the experimental results of cross-anisotropic sands in isotropic compression tests, the principal stress coordinate system is rotated such that the model operates isotropically within the rotated framework. Experimental plastic work contours on the octahedral plane are plotted for a series of true triaxial tests on dense Santa Monica Beach sand to study the effects of cross anisotropy on the evolution of yield surfaces. The amount of rotation of the yield and plastic potential surfaces decreases to zero (isotropic state) with loading. The model is constructed for cases where the principal stress and material symmetry axes are collinear and no significant rotation of principal stresses occur. The model incorporates fourteen parameters that can be determined from simple experiments, such as isotropic compression, drained triaxial compression, and triaxial extension tests. A series of true triaxial and isotropic compression tests on dense Santa Monica Beach sand are used as a basis for verification of the capabilities of the proposed model.     

Effect of Microfabric on Undrained Static and Cyclic Behavior of Kaolin Clay

Microfabric plays an important role in the engineering behavior of soils. Although many studies are available in the literature on the effect of microfabric on the static behavior of soils, the effect on the cyclic behavior is less understood. In the present study, samples with different microfabric were prepared in the laboratory by reconstituting commercially available kaolin clay with different pore fluids under a consolidation pressure of 100?kPa. Consolidated undrained triaxial tests were carried out on these samples under static and cyclic loading conditions. Dispersed samples were found to have monotonic stress-strain behavior with a peak deviatoric stress and higher peak undrained shear strength than the flocculated samples. However, the dispersed samples were found to offer less resistance to cyclic loading. When subjected to cyclic loading, dispersed samples failed within a few cycles under a cyclic stress ratio (defined as the ratio of cyclic deviatoric stress to the undrained shear strength) close to 0.6, whereas in flocculated samples, sudden failure was not observed even at a higher cyclic stress ratio of 0.9, although strains and pore pressures accumulated to higher values. Postcyclic monotonic tests conducted on samples that did not fail under cyclic loading showed an apparent overconsolidation effect caused by cyclic loading in a similar manner, as reported in the literature.     

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.     

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.     

Effects of Principal Stress Rotation on Permanent Deformation in Rail Track Foundations

A realistic assessment of the whole life cost of rail track foundations requires analysis of the effects of the repeated loadings applied by trains. This paper reports the effects of principal stress rotation (PSR) during cyclic loading on the permanent deformations measured in a series of hollow cylinder tests. The tests were carried out on a number of reconstituted soils selected in order to simulate foundation materials on an existing heavy haul railway line. Typical loadings and track geometry together with dynamic finite-element analyses were used to define representative stress changes to be applied to these soils, which were then tested with and without principal stress rotation during loading. It is shown that principal stress rotation has a significant and deleterious impact on permanent deformation of some materials. Therefore, it is concluded that cyclic triaxial testing, which cannot impose principal stress rotation, will not necessarily give good estimates of the long-term performance of rail track foundations. As PSR cannot be ignored when evaluating permanent displacements of rail track foundations, the use of more appropriate (realistic) testing methods such as the cyclic hollow cylinder or the cyclic simple shear apparatus is required.     

Constitutive Model of Soil Based on a Dynamical Systems Approach

A soil when sheared ultimately reaches a steady-state condition at which it deforms at a constant shear stress, effective normal stress, and void ratio. Various systems in nature dynamically evolve similarly from some initial condition, to a final steady-state condition. Such systems have been studied using dynamical systems theory. This technical note uses this theory to model monotonic shear of soil as a dynamical system. The principle proposed is simple—the rates of change of the shear stress, effective normal stress, and void ratio are proportional to the applied values of the shear and effective normal stress with the proportionality values decaying with strain until ultimately these proportionality values become zero at the steady-state condition. It provides a well-formed qualitative principle that fits closely the stress-strain-void ratio curves of undrained shear tests on uncemented, resedimented clays at various over consolidated ratios (OCRs), and drained shear tests on sands and silts at various relative densities, for various stress paths including compression, extension from standard triaxial, and true-triaxial tests. For the undrained shear of resedimented clay, these proportionalities and their decay rates vary smoothly with OCR. For drained shear of sand and silt, the model parameters show orderly variation with relative density. Its value lies in that a well-formed qualitative principle derived from the steady-state condition provides an alternate approach to current complex elastoplastic models based on critical state theory.     

Implicit Algorithm for Modeling Unsaturated Soil Response in Three-Invariant Stress Space

An implicit integration algorithm has been refined to predict the stress–strain–strength response of unsaturated soil under suction-controlled, multiaxial stress paths that are not achievable in a conventional cylindrical cell. The algorithm supports numerical analyses in a deviatoric plane by using a mixed control constitutive driver, in conjunction with a generalized Cam-Clay model that also incorporates the influence of a third stress invariant, or Lode-angle θ, within a constant-suction scheme. True triaxial data from a previously accomplished series of suction-controlled triaxial compression, triaxial extension, and simple shear tests on 10-cm cubical specimens of silty sand, were used for the tuning and validation of the refined algorithm. The elliptical Willam–Warnke surface was adopted for simulation of unsaturated soil response in three-invariant stress space. Reasonably satisfactory agreement was observed between experimental and predicted deviatoric stress versus principal strain response for different suction states, as well as between experimental and predicted strength loci in a deviatoric plane.     

Numerical Study of Impact of Soil Anisotropy on Seismic Performance of Retaining Structure

Recent laboratory investigations indicate that the stress–strain–strength responses of granular soils are appreciably affected by the fabric orientation of the soil relative to the frame of principal stresses. Especially, a sand specimen exhibiting a dilative response during triaxial compression may show a contractive response during triaxial extension under otherwise identical conditions. This observation is of practical importance for applications concerning essentially undrained loading conditions, because the effective mean normal stress at failure, and consequently, the shear strength, associated with an undrained contractive path are considerably lower than those following a dilative path. This raises a question about the impact of soil anisotropy on seismic performance of retaining structures subjected to active and passive earth pressures, because the directions of principal stresses in retained soils for the two cases are very different. This note presents a set of fully coupled finite-element analyses incorporating an anisotropic sand model. The analyses reveal that the impact of fabric anisotropy could be significant when the retaining structure is under passive earth pressure conditions.     

Effect of Loading Mode on Strain Softening and Instability Behavior of Sand in Plane-Strain Tests

Experimental data to study the effect of loading mode on the strain softening and instability behavior of sand under plane-strain conditions are presented in this paper. A new plane-strain apparatus was adopted to conduct K0 consolidated drained and undrained tests under both deformation-controlled and load-controlled loading modes. The drained behavior of very loose and medium dense sand and the undrained behavior of very loose sand under plane-strain conditions were characterized. The test results show that the loading mode affects the postpeak behavior and controls whether strain softening or instability will occur in the postpeak region. Shear bands occurred in tests conducted on medium dense sand, but not in tests for very loose sand. The failure line and critical state line are not affected by the loading mode. The study also shows that the concept of a unique “ultimate state” for both dense and loose sand as previously established based on conventional drained triaxial tests is not supported by the plane-strain data.     

Influence of Stress Ratio and Stress Path on Behavior of Loose Decomposed Granite

This paper presents results from four series of triaxial compression tests of loosely compacted decomposed granite (DG) or silty sand on both isotropically and anisotropically consolidated specimens. These tests included undrained tests, drained tests with constant deviator stress, and a decreasing mean effective stress path. The silty sand possessed high compressibility during isotropic compression. The observed high compressibility is probably attributed to the loose soil structure created by using the moist tamping method and the presence of crushable feldspar in the soil. Static liquefaction behavior and the so-called “reversed” sand behavior were observed in all undrained tests. This “reversed” sand behavior can be readily explained by the high compressibility of DG leading to the nonparallel and converging nature of the initial state line and the critical state line. Preshearing resulted in a more brittle response in the postpeak behavior. The higher the initial stress ratio (ηc), the smaller the ductility. Structural collapse of DG was observed. This collapse is characterized by a sudden large increase in both the axial and contractive volumetric strains. The mobilized angles of friction at collapse range from 31.8° to 38.7°, which are smaller than the critical state angle (?col′), but higher than the mobilized friction angle of the instability line (28.1°) determined by the isotropically consolidated undrained tests. A trilinear approximate relationship can be found between ?col′ and ηc and a liquefaction potential index is introduced to provide a simple preliminary design parameter for static liquefaction and instability prone slopes.     

Elastoplastic Model for Clay with Microstructural Consideration

Clay material can be considered as a collection of clusters, which interact with each other mainly through mechanical forces. From this point of view, clay is modeled by analogy to granular material in this paper. An elastoplastic stress-strain relationship for clay is derived by using the granular mechanics approach developed in previous studies for sand. However, unlike sand, clay deformation is generated not only by the mobilizing but also by compressing clusters. Thus, in addition to the Mohr-Coulomb’s plastic shear sliding and a dilatancy type flow rule, a plastic normal deformation has been modeled for two clusters in compression. The overall stress-strain relationship can then be obtained from the mobilization and compressing of clusters through a static hypothesis of the macro-micro relations. The predictions are compared with the experimental results for clay under both drained and undrained triaxial loading conditions. Three different types of clay, including remolded and natural clay, have been selected to evaluate the model’s performance. The comparisons verify that this model is capable of accurately reproducing the overall behavior of clay, which accounts for the influence of key parameters such as void ratio and mean stress. A section of this paper is devoted to show the model’s capability of considering the influence of inherent anisotropy on the stress-strain response under undrained triaxial loading conditions.     

Comparison in Undrained Shear Strength between Undisturbed and Remolded Ariake Clays

Triaxial consolidation undrained shear tests are performed on both undisturbed and remolded Ariake clays to investigate the undrained shear strength behavior. When the applied confining stress is larger than the triaxial consolidation yield stress, the strength envelopes expressed in the plot of undrained shear strength versus confining stress of both the undisturbed and the remolded Ariake clays are straight lines through the origin. The strength envelope of the remolded Ariake clays lies above that of the undisturbed Ariake clays when the applied confining stress is larger than the consolidation yield stress. This difference is caused by the difference in water content between undisturbed and remolded states. When the data obtained from triaxial consolidation undrained shear tests of both the undisturbed and the remolded Ariake clays are plotted in the plot of undrained shear strength versus water content, it is found that the undrained shear strength decreases uniquely with the increase in water content.     

Characterization of Failure in Cross-Anisotropic Soils

Drained true triaxial tests on dense Santa Monica Beach sand deposited with a cross-anisotropic fabric have been performed to study the failure condition in the principal stress space. The failure surface was assumed to be symmetric around the vertical axis (on the octahedral plane of the principal stress space), but varying as a function of the Lode angle. Data from previously performed consolidated-undrained true triaxial tests on San Francisco Bay Mud and data from triaxial compression, triaxial extension, and plane strain tests on Toyoura sand showed similar behavior in terms of effective stresses. A three-dimensional failure criterion is proposed for characterization of failure in cross-anisotropic soils, under commonly occurring conditions when loading and depositional directions coincide and no significant rotation of principal stresses occur. This cross-anisotropic criterion is developed using a coordinate rotation of the principal stress space and utilization of an existing isotropic failure formulation. Derivation of the three required parameters is explained and illustrated. The proposed criterion is compared with various experimental results; and it is demonstrated that the failure criterion for cross-anisotropic soils captures the experimental behavior with good accuracy.     

Undrained Shear Strength of Pleistocene Clay in Osaka Bay

This study presents the undrained shear characteristics of Holocene and Pleistocene clay samples from depths of 20–200 m under the seabed in Osaka Bay. Automated triaxial K0 consolidation tests and anisotropically consolidated-undrained triaxial compression and extension tests are conducted using the recompression method. The average undrained strength ratio (su/σv0′) is 0.33 (SD = 0.03) when the extension strength is defined as the peak strength or the strength at an axial strain of 15%, while su/σv0′ is 0.29 (SD = 0.04) when the extension strength is defined as the shear stress at the axial strain corresponding to the peak compression strength. Circular arc stability analyses are carried out with the modified Fellenius and Bishop methods for the design cross section of the seawall structure of the Kansai International Airport to study the effects of different definitions of shear strength. The seawall is founded on 19 m of soft Holocene clay and 10 m of Pleistocene sand overlying the Pleistocene clay. The stability analyses show that the factor of safety and depth of the critical circle (i.e., above versus below the sand layer) are sharply affected by both the value of su/σv0′ (0.33 versus 0.29) and the method of slices (Fellenius versus Bishop). The marginal stability calls for careful monitoring of construction with field instrumentation.