Dilatancy and Shear Strength of Sand at Low Confining Pressures

Sand dilates with shearing at a rate that increases with increasing relative density (DR) and decreases with increasing effective confining stress (σc′). The peak friction angle of a sand depends on its critical-state friction angle and on dilatancy. In this paper, we develop a simple correlation between peak friction angle, critical-state friction angle, and dilatancy based on triaxial compression and plane-strain compression test data for sand for a range of confining pressures from very low levels to approximately 196 kPa.     

Shaft Resistance of Single Vertical and Batter Piles Driven in Sand

An experimental investigation of the shaft resistance of single vertical and batter piles pushed into sand was conducted. A prototype laboratory setup was designed for testing relatively large model piles, inclined at an angle that varied between zero and 30° with the vertical. Two model piles having diameters of 38 and 76 mm were tested at a ratio of the pile’s length to diameter up to 40, and subjected to axial compression loading. The pile models were instrumented to allow direct measurements of the shaft resistance. A theoretical model was developed to take into account the asymmetrical earth pressure distribution around the pile shaft, the level of mobilization of the angle of friction between the pile shaft and the sand, and the pile diameter. The results predicted by the theory developed agreed well with the experimental results of the present investigation as well as other experimental and field results available in the literature. Design charts are presented for use in practice. The results of the present investigation support the concept of the critical depth for the shaft resistance of vertical and batter piles driven in sand.     

Design of a Rigid Cutoff Wall

A sheet pile cutoff wall simply called cutoff wall is used in almost all types of water retaining structures to reduce the exit gradient at the downstream toe and prevent the chances of sand boiling and piping. In 1954, Terzaghi has suggested a simplified approach for the design of cutoff walls considering average seepage force. In Terzaghi’s approach, the unbalanced water pressure around the cutoff wall is coupled with the active earth pressure and the resultant thrust is determined by subtracting the passive thrust from the combined active thrust. The value of passive earth pressure coefficient has been assumed to correspond with a downstream failure wedge having an angle of (45°?1/2) with the horizontal, where 1 = effective angle of internal friction of the foundation soil. In this paper, it is shown that under steady state flow conditions for a flexible levee base, failure does not take place always at this angle. Considering exact seepage forces and applying the laws of equilibrium, active and passive earth pressures acting on a rigid sheet pile cutoff wall on an impervious levee have been determined. The weight of the levee has been considered in the computation of active thrust. The design procedure of a rigid cutoff wall is also explained. There is a difference of approximately 10% between the passive thrusts for a rigid cutoff wall of normal length computed by Terzaghi’s method and by the rigorous method presented herein.     

Postpeak Strength of Interfaces in a Stress-Dilatancy Framework

Laboratory sand-steel interface tests, using a range of sand sizes on a wide range of surface roughnesses, have been conducted using a direct shear apparatus modified to enable reliable measurements of both friction and dilation. The paper looks at the minimum interface strength after peak, termed here the postpeak strength, and assesses its dependence on roughness, density, and stress level. Its upper limit is the large displacement direct shear friction angle, related to but not equal to the critical state friction angle. When data are normalized by this value, they show linear dependence on the logarithm of relative roughness in the intermediate zone between smooth and rough. Once the roughness dependence of the postpeak strength has been allowed for, dilatant interfaces are found to follow classical stress–dilatancy relationships. It appears that there is no fundamental difference in the responses of sand-on-steel or sand-on-sand interfaces.     

Pile Bearing Capacity Factors and Soil Crushabiity

The existence of large magnitude stresses at the tip of a bearing pile is a well known phenomenon leading to crushing of soil grains and thus affecting pile behavior. Classical foundation design calculations which assume that the soil fails in shear and neglect volume change can be safely used where stress levels or particle strengths prevent crushing, however in the case of weak grains or high foundation stresses consideration should be given to the effects of grain crushing and the resulting volumetric compression. Model pile tests have been carried out in two skeletal carbonate sands and a standard silica sand with the aim of examining the variation of skin friction and end bearing capacities with degree of penetration. The mobilization of the strength of crushable soils requires a much higher strain level while at the same time the end bearing pressure on the model piles exceeded 10?MPa inducing considerable particle breakage. The peak skin friction for all sands occurred at a settlement normalized by pile diameter, S/D, of less than 0.1. At this point the carbonate sands generally had lower skin friction values than the silica sand. Further displacement caused a rapid decrease in skin friction for all three materials. At higher lateral stresses the less crushable Toyoura silica sand generated higher skin frictions. Samples of Chiibishi sand were sectioned and photographed. It was observed that a spherical plastic zone was formed at the base of the pile which expanded with increasing S/D and a degraded layer of broken particles developed around the pile as S/D increased. Large values of the Marsal particle breakage factor were restricted to a zone extending outwards to one pile radius. An end bearing capacity modification factor has been proposed to adapt the conventional bearing capacity equation for soil crushability. This modification factor is a function of soil compressibility and degree of penetration. The factor was shown to decrease with increasing soil compressibility and increase with normalized penetration S/D.     

Computation of Cavity Expansion Pressure and Penetration Resistance in Sands

A cavity expansion-based theory for calculation of cone penetration resistance qc in sand is presented. The theory includes a completely new analysis to obtain cone resistance from cavity limit pressure. In order to more clearly link the proposed theory with the classical cavity expansion theories, which were based on linear elastic, perfectly plastic soil response, linear equivalent values of Young's modulus, Poisson’s ratio and friction and dilatancy angles are given in charts as a function of relative density, stress state, and critical-state friction angle. These linear-equivalent values may be used in the classical theories to obtain very good estimates of cavity pressure. A much simpler way to estimate qc—based on direct reading from charts in terms of relative density, stress state, and critical-state friction angle—is also proposed. Finally, a single equation obtained by regression of qc on relative density and stress state for a range of values of critical-state friction angle is also proposed. Examples illustrate the different ways of calculating cone resistance and interpreting cone penetration test results.     

Passive Earth Pressure with Critical State Concept

This paper presents experimental data of earth pressure acting against a vertical rigid wall, which moved toward a mass of dry sand. The backfill had been placed in lifts to achieve relative densities of 38, 63, and 80%. The instrumented retaining-wall facility at National Chiao Tung University in Taiwan was used to investigate the effects of soil density on the development of earth pressure. Based on the experimental data, it has been found that the Coulomb and Terzaghi solutions calculated with the peak internal friction angle significantly overestimated the ultimate passive thrust for the retaining wall filled with dense sand. As the wall movement S exceeded 12% of the wall height H, the passive earth thrust would reach a constant value, regardless of the initial density of backfill. Under such a large wall movement, soils along the rupture surface had reached the critical state, and the shearing strength on the surface could be properly represented with the residual internal-friction angle. The ultimate passive earth pressure was successfully estimated by adopting the critical state concept to either Terzaghi or Coulomb theory.     

State-Dependent Strength of Sands from the Perspective of Unified Modeling

This paper discusses the state-dependent strength of sands from the perspective of unified modeling in triaxial stress space. The modeling accounts for the dependence of dilatancy on the material internal state during the deformation history and thus has the capability of describing the behavior of a sand with different densities and stress levels in a unified way. Analyses are made for the Toyoura sand whose behavior has been well documented by laboratory tests and meanwhile comparisons with experimental observations on other sands are presented. It is shown that the influence of density and stress level on the strength of sands can be combined through the state-dependent dilatancy such that both the peak friction angle and maximum dilation angle are well correlated with a so-called state parameter. A unique, linear relationship is suggested between the peak friction angle and the maximum dilation angle for a wide range of densities and stress levels. The relationship, which is found to be in good agreement with recent experimental findings on a different sand, implies that the excess angle of shearing due to dilatancy in triaxial conditions is less than 40% of that in plane strain conditions. A careful identification of the deficiency of the classical Rowe’s and Cam-clay’s stress–dilatancy relations reveals that the unique relationship between the stress ratio and dilatancy assumed in both relations does not exist and thereby obstructs unified modeling of the sand behavior over a full range of densities and stress levels.     

Postshaking Shear Strain Localization in a Centrifuge Model of a Saturated Sand Slope

This paper presents analyses of a test conducted on a 9-m-radius centrifuge to study the redistribution of pore water during diffusion of earthquake-induced excess pore pressures in a sand slope with embedded silt layers. The centrifuge model developed large postshaking deformations associated with shear strain localization at the interface between the sand and silt layers. Dense arrays of pore pressure transducers provided detailed measurements of pore pressure variations in time and space within the slope. A new data analysis approach is presented in which measured pore-pressures are used to compute flow rates and volumetric strains as a function of time and position throughout the slope. Hydraulic gradients were calculated by numerical differentiation of measured pore-pressure distributions with respect to position. Flow rates that were based on Darcy’s law were then integrated with respect to time to obtain flow quantities, from which volumetric strains were computed. A second data analysis approach that computes volumetric strains on the basis of soil compressibility and changes in pore pressure provided an independent computation of strains in consolidating zones. Results using these data analysis procedures confirm that a dilating (loosening) zone of significant thickness developed in the sand immediately beneath an embedded silt layer that had impeded the drainage of high pore pressures. These results support the hypothesis that the dilating zone corresponds to regions where the mobilized friction angle exceeds the critical state friction angle and that the dilating zone can be initially relatively thick before its size diminishes to the thickness of a thin shear band after the peak friction angle is mobilized. Quantification of the evolution of the size of the dilating zone is a key to understanding the magnitude of deformations associated with void redistribution.     

Assessment of the Undrained Response of Sands under Limited and Complete Liquefaction

The technique presented deals with the assessment, based on drained test behavior and formulation, of the undrained postcyclic stress-strain behavior of sands under limited or complete (full) liquefaction and its associated strength. At present, there is no particular procedure that allows assessment of such undrained postcyclic behavior that could develop full (pore-water pressure ratio, ru = 1) or limited (ru<1) liquefaction. The prediction of the undrained postliquefaction (full or limited liquefaction) response presented here is based on basic properties of sand such as its relative density (Drc) [or (N1)60 blowcount], the effective angle of internal friction (φ), the roundness of the sand grains (ρ), and the drained axial strain at 50% stress level (ε50). The technique presented accounts for the excess pore-water pressure induced by cyclic loading (Δuc) and the postcyclic excess pore-water pressure generated under undrained monotonic loading (Δud).     

Effect of Arching on Uplift Capacity of Pile Groups in Sand

In this paper an analytical method has been proposed to predict the net ultimate uplift capacity of pile groups embedded in sand considering the arching effect. This method takes into consideration the embedded length (L), diameter of the pile (d), surface characteristics of pile, group configuration, spacing of the pile group (3d to 6d), and the soil properties. Arching develops due to relative compressibility of sand relative to pile which activates the soil–pile friction. As piles/pile groups move up, the active state of soil is initiated. The modified value of active earth pressure coefficient considering arching effect has been derived. Typical charts for evaluation of net ultimate uplift capacity for pile groups are presented through the figures. The predicted values of ultimate uplift capacity of pile groups with different configuration and slenderness ratios are compared with the available experimental results. The predicted values considering arching effect are found to be in good agreement with the data available from the literature.     

Ultimate Lateral Resistance of Pile Groups in Sand

Experimental investigations on model pile groups of configuration 1 × 1, 2 × 1, 3 × 1, 2 × 2, and 3 × 2 for embedment length-to-diameter ratios L∕d = 12 and 38, spacing from 3 to 6 pile diameter, and pile friction angles δ = 20° and 31°, subjected to lateral loads, were conducted in dry Ennore sand obtained from Chennai, India. The load-displacement response, ultimate resistance, and group efficiency with spacing and number of piles in a group have been qualitatively and quantitatively investigated. Analytical methods have been proposed to predict the ultimate lateral capacity of single pile and pile groups. The proposed methods account for pile friction angle, embedment length-to-diameter ratio, the spacing of piles in a group, pile group configuration, and soil properties. These methods are capable of predicting the lateral capacity of piles and pile groups reasonably well as noted and substantiated by the comparison with the experimental results of the writers and other researchers.     

Influence of Optimized Tire Shreds on Shear Strength Parameters of Sand

This paper presents the usefulness of optimizing the size of waste tire shreds on shear strength parameters of sand reinforced with shredded waste tires. A relatively, uniform sand has been mixed with randomly distributed waste tire shreds with rectangular shape and compacted at 2° of compaction. Waste tire shreds were prepared with a special cutter in three widths of 2, 3, and 4?cm and various lengths for each shred width. Three shred contents of 15, 30, and 50% by volume were chosen and mixed with the sand to obtain a uniformly distributed mixture. In order to compare the shear strength of different sand–tire shred samples, two compaction efforts in terms of sand matrix unit weights of 15.5 and 16.8?kN/m3 were considered. The results show that the influencing parameters on shear strength characteristics of sand–shred mixtures are normal stress, sand matrix unit weight, shred content, shred width, and aspect ratio of tire shreds. With the selected widths of shreds, compaction efforts, shred contents, and the variations of aspect ratios, it is possible to increase the initial friction angle ?1 up to 113.5%, that is ?1 = 67°. The average value for the influence of aspect ratio variations on increase in friction angle of the mixtures for all tests has been found to be about 25%. These average values for lower and higher compacted samples containing different widths and aspect rations were 37.6 and 17.2%, respectively. It has been investigated that for a given width of tire rectangular shreds, there is solely a certain length, which gives the greatest initial friction angle for sand–tire shred mixtures. This is the main contribution of this paper.     

Base Resistance of Jacked Pipe Piles in Sand

The paper presents the results from an experimental program carried out at Trinity College Dublin, in which instrumented model piles were jacked into loose dry sand in a large testing chamber. A number of pile installations were carried out to study the effects of in situ stress, diameter, and wall thickness on the behavior of open-ended piles in sand. These indicated that plug stiffness and capacity may be expressed as simple functions of the cone penetration test end resistance and the incremental filling ratio prior to loading. The magnitude and distribution of shear stresses measured on the inner wall are shown to be compatible with existing experimental data and can be related directly to the stress level, interface friction angle, and dilation of the sand at the pile wall. The data are shown to facilitate a better understanding of the factors controlling plug resistance.     

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.     

Prediction of Soil Properties from the Concepts of Energy Transfer in Dynamic Penetration Tests

Results from dynamic penetration tests are traditionally interpreted on the basis of empirical correlations, this being a frequent criticism to these tests. An alternative rational method of interpretation is proposed in this paper from which the energy delivered to the composition of rods is used to calculate a dynamic force that represents the reaction of the soil to the penetration of the sampler (Fd). Interpretation of soil properties both in sand and clay is based on this calculated dynamic force from which the internal friction angle and the undrained shear strength can be estimated. This is achieved from a simple combination of limit equilibrium analysis and cavity expansion theory. Case studies gathered from the Brazilian experience are reported in this paper to illustrate the applicability of the proposed approach.     

Tensile Strength of Unsaturated Sand

A theory that accurately describes tensile strength of wet sand is presented. A closed form expression for tensile strength unifies tensile strength characteristics in all three water retention regimes: pendular, funicular, and capillary. Tensile strength characteristically increases as soil water content increases in the pendular regime, reaches a peak in the funicular regime, and reduces with a continuing water content increase in the capillary regime. Three parameters are employed in the theory: internal friction angle (at low normal stress) ?t, the inverse value of the air-entry pressure α, and the pore size spectrum parameter n. The magnitude of peak tensile strength is dominantly controlled by the α parameter. The saturation at which peak tensile strength occurs only depends on the pore size spectrum parameter n. The closed form expression accords well with experimental water retention and tensile strength data for different sands.     

Seismic Displacement Criterion for Soil Retaining Walls Based on Soil Strength Mobilization

This paper presents a seismic displacement criterion for conventional soil retaining walls based on the observations of a series of shaking table tests and seismic displacement analysis using Newmark’s sliding-block theory taking into account internal friction angle mobilization along the potential failure line in the backfill. A novel approach that relates the displacement of the wall and the mobilized friction angle along the shear band in the backfill is also proposed. A range of horizontal displacement-to-wall height ratios (δ3h/H) between 2 and 5% representing a transitional state from moderate displacement to catastrophic damage were observed in the shaking table tests on two model retaining walls. This observation is supported by both Newmark’s displacement analysis and a new approach that relates the movement of the wall to the mobilization of the friction angle along the shear band in the backfill. A permissible displacement of the wall as defined by the displacement-to-wall height ratio, namely, δ3h/H, equal to 2% was found to be of practical significance in the sense that peak friction angle of the investigated sand is retained along the shear band in the backfill. It is also suggested that δ3h/H = 5% be used as a conservative indicator for the onset of catastrophic failure of the wall associated with fully softened soil strength along the shear band in cohesionless backfill.     

Reappraisal of Size Effect of Bearing Capacity from Plastic Solution

A simplified method for estimating the ultimate bearing capacity of surface footings on sand is described with special attention to the dependency of the angle of internal friction of sand on confining stress. An extended slip line method is developed, in which the dependency of the angle of internal friction on the confining stress is formulated from results of conventional triaxial compression tests for various sands. Based on results from a comprehensive series of calculations employing the extended slip line method, the writers reappraise size effects on bearing capacity and investigate the relationship between strength parameters of sand and size effects on bearing capacity. A modified formula and several diagrams that provide a simple estimation method are proposed to consider size effects on bearing capacity. A comparison between estimations using the formula and ultimate bearing capacities measured from several series of centrifuge tests demonstrates the practicability of the proposed method for both strip and circular footings.