Rowe's Stress-dilatancy Research Articles

On the modelling of stress-dilatancy behavior in weakly cemented sands

A comprehensive study on the stress-dilatancy behavior of cemented sand and its modeling is presented. The effect of confining pressure, relative density, and cement content on stress-dilatancy behavior are studied from the published experimental results and an additional series of experiments performed in this study. To facilitate a contrast and comparison of stress-dilatancy behavior between these datasets, a normalized stress ratio is proposed which removes the effect of mineralogy and morphology of parent sand. A set of key insights were obtained from this comparative study which aided in improving the stress-dilatancy relation; for example, the effect of initial conditions on stress-dilatancy behavior was found to be captured by the ratio of cohesion intercept (or tensile strength) and mean effective stress before shearing. The limitations of stress transformation, often used in modelling of cemented sand, were also systematically studied by a set of carefully designed experiments; it was found to be only applicable before gross yielding of cementation. After gross yielding, it is necessary to take in account of the breakage of bonds/cementation. The gross yield locus was identified from 70 experimental datasets and a cohesion/bond degradation model was formulated to model the stress-dilatancy behavior of cemented sand. The efficacy of stress-dilatancy relations (after including the gross yield locus and bond degradation behavior) is evaluated from the experimental results; the Rowe's stress-dilatancy relation was found to be most suitable with the proposed bond/cohesion degradation model.

Influence of particle shape on the microstructure evolution and the mechanical properties of granular materials

In order to study the influence of particle shape on the microstructure evolution and the mechanical properties of granular materials, a two-dimensional DEM analysis of samples with three particle shapes, including circular particles, triangular particles, and elongated particles, is proposed here to simulate the direct shear tests of coarse-grained soils. For the numerical test results, analyses are conducted in terms of particle rotations, fabric evolution, and average path length evolution. A modified Rowe's stress–dilatancy equation is also proposed and successfully fitted onto simulation data.

A modified elasto-plastic model with double yield surfaces and considering particle breakage for the settlement analysis of high rockfill dams

This paper improves the elasto-plastic model with double yield surfaces in the context of the hardening soil model for the simulation of the settlement behavior of high rockfill dams. The stress-dependent stiffness values (E50 and Eoed control the shear hardening and the cap yield surfaces, respectively) are modified to exhibit different degrees of evolution with changes in the stress state. A modification of Rowe's stress-dilatancy theory is proposed to account for the influence of particle breakage. Good quantitative agreement between simulated and measured stress-strain relationships can be achieved; in particular, the volumetric strain is much improved from the original model. The developed model is applied to predict the settlement of Nam Ngum 2, a 182 m high rockfill dam, during the construction stage, in conjunction with a three-Dimensional (3D) Finite Element (FE) analysis. The findings show that a good agreement between computed settlements and dam field monitoring data can be achieved.

Relationships between chemical weathering indices and physical and mechanical properties of decomposed granite

Chemical weathering is one of the dominant mechanisms for weathering of granite in subtropical and tropical regions resulting in modifications of its chemical, physical and mechanical properties. Thus, the changes in chemical properties may provide insight about the changes in physical and mechanical properties of weathered granite. In this paper three quantitative chemical weathering indices are correlated to the dry density of decomposed granite. A linear relationship is found between each chemical weathering index and dry density for granitic saprolites. Mobiles index (Imob) gives the highest coefficient of correlation among the three chemical weathering indices. Further investigations were conducted to establish the relationships between Imob and other physical and mechanical properties of granitic saprolites. The test results showed that fines content increases with increasing Imob, but peak strength increases with decreasing Imob. The peak states of granitic saprolites are consistent with Rowe's stress–dilatancy relationship. Dilatancy increases with decreasing Imob that contributes to a higher peak strength. Based on some test results presented in this study, it seems that Imob could be a good indicator to quantify the effects of chemical weathering on physical and mechanical properties of granitic saprolites.

Microstructural formulation of stress dilatancy

In this work, we show that the well-known Rowe's stress-dilatancy relation can be readily recovered from a micromechanical analysis of an assembly of rigid particles as a purely dissipative system in the case of a regular packing. When the analysis is extended to a random packing, one can explicitly incorporate the dependence of fabric, density and stress level on dilatancy, a basic aspect of geomaterial behaviour. The resulting microstructurally based stress dilatancy relation can be easily implemented as a non-associated flow rule in any standard elastoplastic model. Some numerical simulations of stress-dilatancy with initial fabric as a controlling variable are presented to illustrate the developed model.

Stress–dilatancy relation for Mohr–Coulomb soils following a non-associated flow rule

Rowe's stress–dilatancy relation for frictional (cohesionless) materials has been a cornerstone of soil mechanics. The original derivation of this relationship was based on incorrect energy minimisation considerations, but the relationship was proven later by De Josselin de Jong using friction laws, and has been confirmed by a large body of experimental results. In contrast, the validity of Rowe's stress–dilatancy relation for cohesive-frictional materials, which has also been used, although not as extensively, was never verified. This paper shows that Rowe's stress–dilatancy relation for Mohr–Coulomb soils (cohesive-frictional materials) is in fact incorrect. The paper also provides a correct stress–dilatancy relationship for non-associated Mohr–Coulomb soils that have both cohesive and frictional strength components. The derivation of the relationship for cohesive-frictional soils presented in this paper relies on use of the sawtooth model together with the application of the laws of friction.

A graphical method for producing yield surfaces for soils

A procedure is described by which three-dimensional yield criteria and flow rules can be derived graphically by drawing envelopes. Using computer graphics, this provides the modeller with a simple, clear, precise and flexible method with which to generate data that can be compared with results obtained analytically or experimentally. As illustrative examples, yield surfaces are constructed in the constant-pressure plane in principal stress space using the Drucker–Prager and Frossard's dissipation functions, and two modified forms of Houlsby's dissipation function. For constant-volume flow these produce the Drucker–Prager, Mohr–Coulomb and Matsuoka–Nakai yield surfaces. Each is paired with both an isotropic and an anisotropic dilatancy rule. The direction of plastic flow at yield, consistent with the choice of dissipation function and dilatancy rule, can be determined from these constructions. One of the yield surfaces produced is compared with the results from true triaxial tests where the rate of dilatancy has been determined. An example of Rowe's stress–dilatancy plots is also produced.

The shearing behaviour of a sugar aggregate

To better understand the behaviour of sugar within industrial centrifuges or silos, drained triaxial tests were performed on loose, dry or moist sugar aggregates under low confining pressures (15–90 kPa). Particular attention is paid to test reproducibility and grain damage level. Rowe's stress-dilatancy theory is used to improve characterisation of the critical state, at which the aggregate of grains could participate in frictional flow at constant volume. The effects of strain rate, mean grain size and moisture upon internal friction and dilatancy are each investigated. Additionally, initial elastic properties are identified.

Cavity expansion in cemented materials: structure degradation effects

A numerical solution of a cylindrical cavity expansion problem is presented herein, which is formulated within the framework of non-associated plasticity. The work extends the solution proposed by Mántaras & Schnaid in a companion paper in which a drained analysis has been developed based on postulates embedded on Rowe's stress dilatancy theory. This new formulation aims at demonstrating the significance of structure degradation during shear for a bonded cohesive-frictional material. The proposed solution makes it possible to derive the continuous variations of strains, stresses and volume changes produced around an expanding cavity. The significance of the method is demonstrated by a parametric study designed to highlight the influence of strength reduction during shear on cavity expansion analysis.

Cavity expansion in cemented materials: structure degradation effects

A numerical solution of a cylindrical cavity expansion problem is presented herein, which is formulated within the framework of non-associated plasticity. The work extends the solution proposed by Mántaras & Schnaid in a companion paper in which a drained analysis has been developed based on postulates embedded on Rowe's stress dilatancy theory. This new formulation aims at demonstrating the significance of structure degradation during shear for a bonded cohesive-frictional material. The proposed solution makes it possible to derive the continuous variations of strains, stresses and volume changes produced around an expanding cavity. The significance of the method is demonstrated by a parametric study designed to highlight the influence of strength reduction during shear on cavity expansion analysis.

Determination of plane-strain shear strength of sand from the results of triaxial tests

Experimental investigation of the shear strength of dry sands was carried out using triaxial and plane-strain apparatus. The results were used to evaluate Rowe's stress–dilatancy theory, the relationships between the shear strength components due to friction and interlocking, and the volume-change characteristics for cases of plane-strain and axisymmetric boundary conditions. Because of the complexity of the plane-strain testing apparatus in the normal soil mechanics laboratory and the difficulties involved in performing this type of shear test, it is becoming costly to obtain plane-strain test results for consulting purposes. Based on Rowe's stress–dilatancy theory, the results of the present investigation, and the available test results in the literature, two simple methods are proposed to predict the angle of shearing resistance for plane-strain conditions from the results of the conventional triaxial compression tests.Key words: shear strength, plane-strain test, triaxial test, sand, experimental investigation, geotechnical engineering.

Interpretation of pressuremeter tests in sand

This paper presents a method to obtain the constitutive relationships of sand from drained self-boring pressuremeter tests. Plane-strain conditions and Rowe's stress–dilatancy theory are assumed to hold to determine stress and finite strain distributions and paths. The proposed method, which has been validated using both calibration chamber studies and field tests, appears to correctly render the response behaviour of relatively loose to dense sands.Key words: stress–strain relations, self-boring pressuremeter tests, sands, finite strains, stress distributions, paths.

The strength of unsaturated bentonite-enhanced sand

A modification to Rowe's stress-dilatancy equation is presented that extends its range of application to include unsaturated soil behaviour. The results of a programme of constant water content triaxial tests on unsaturated bentonite-enhanced sand (BES) are reported, together with those of a programme of saturated drained triaxial tests on the sand. It is shown that the variation in the rate of dilation at failure with the sand relative density is similar for the two materials. It is proposed that the packing and friction angle of the sand particles and the degree of saturation control the shear strength of unsaturated BES containing modest amounts of bentonite, and that the shear strength of the bentonite component can be ignored.

The strength of unsaturated bentonite-enhanced sand

A modification to Rowe's stress-dilatancy equation is presented that extends its range of application to include unsaturated soil behaviour. The results of a programme of constant water content triaxial tests on unsaturated bentonite-enhanced sand (BES) are reported, together with those of a programme of saturated drained triaxial tests on the sand. It is shown that the variation in the rate of dilation at failure with the sand relative density is similar for the two materials. It is proposed that the packing and friction angle of the sand particles and the degree of saturation control the shear strength of unsaturated BES containing modest amounts of bentonite, and that the shear strength of the bentonite component can be ignored.

Prediction of Permanent Deformation of Asphalt Concrete in Cyclic and Monotonic Loading

Abstract New theoretical developments are presented to predict the permanent deformation in asphalt concrete caused by constant-load creep and by cyclic loads. The constitutive model utilizes multi-yield surfaces and isotropic hardening. A new hardening law for the changes in the values of the plastic moduli during monotonic or cyclic loading is derived from Rowe's stress-dilatancy theory. A complete description of the permanent deformation of asphalt concrete under constant load creep and cyclic loading is given, including the elastic, viscoelastic, plastic, and microcracking components, to predict the permanent deformation under cyclic loading. The model parameters have clearly defined physical meanings and can be determined from simple conventional laboratory tests. A computer program called RUT determines the permanent deformation. There is good agreement between the model predictions and the experimental data.

Model Prediction of Rutting in Asphalt Concrete

A new elastoplastic model is presented for predicting the stress-strain response of asphalt concrete under cyclic loading. The model utilizes multiyield surfaces and isotropic hardening. Rowe's stress dilatancy theory is used to obtain the relationship between the permanent volumetric and vertical strains as well as the hardening law for the changes in the sizes of the plastic moduli caused by cyclic loading. These relationships considerably simplify the task of predicting the plastic deformation under cyclic loading of both triaxial compression and extension tests. A complete description of the plastic deformation of asphalt concrete under cyclic loading is treated, including the elastic, viscoelastic, and plastic components as well as the relationship between rutting and cracking. A computer program, called Rutting in Asphalt Concrete (RUT), determines the plastic deformation under cyclic loading. Good agreement exists between the model predictions and experimental data that include data published by other researchers.

A simple constitutive model for granular soils: Modified stress-dilatancy approach

The dependencies of granular soil behaviour on void ratio and stress are modelled within plasticity theory enriched by a modified stress-dilatancy law. Simplicity has been kept in the development of the constitutive law for easy future implementation in afinite element code. By using a void ratio dependent factor which measures the deviation of the current void ratio from the critical one, Rowe's stress dilatancy equation is modified. This modification indeed corresponds to a new energy dissipation equation for a granular assembly which sustains kinematical constraints under the action of stresses. The proposed constitutive law predicts in a very consistent manner the response of sands in monotonic loading conditions for a large range of initial void ratios and confining pressures without the need to make any adjustments to the material parameters. Well known published data for the drained triaxial compression of Sacramento River sand was successfully modelled.

The effect of end restraint on volume change and particle breakage of sands in triaxial tests : Ueng, T; Tzou, Y; Lee, C Proc symposium on advanced triaxial testing of soil and rock, Louisville, 19–20 June 1986 P679–691. Publ Philadelphia: ASTM, 1988 (ASTM Special Technical Publication 977)

The distributions of volume change and particle breakage within specimens were compared for uniform sands in drained triaxial tests with and without lubricated end platens. The results showed that the volume change at failure, either dilation or compression, of the sands was slightly higher for lubricated specimens at a higher failure strain than for unlubricated specimens, and the difference was proportional to the total volume change at failure. The sands exhibited insignificant differences in uniformity of volume change for specimens with and without lubricated ends under loading before the peak strength. However, a distinctly larger volume change at the middle portion of unlubricated specimens was observed after the loading reached the peak strength. Similar results were obtained for the particle breakage within the specimens in triaxial tests. End lubrication induced more uniform particle breakage of sands after the peak strength was reached. Finally, Rowe's stress-dilatancy theory was evaluated with considerations of dilatancy factor and particle breakage. Particle breakage was found very important in considering strength and volume change of sands.

Response of Granular Soil along Constant Stress Increment Ratio Path

The stress‐strain response of a granular soil along constant stress increment ratio paths is experimentally investigated for the condition of σ2=σ3. Since the strains manifested along such paths can be very small, several measures have been developed to improve the accuracy of the strain measurements. A more accurate method of isolating the elastic strain has also been developed to enable reliable determination of plastic strain increment ratio. Test data unambiguously indicate that the elastic response is anisotropic, and the degree of anisotropy increases with the principal stress ratio. The plastic strain increment ratio so deduced from test data is dependent on the stress increment ratio, but can be predicted by combining Rowe's stress dilatancy equation and the energy equation of the Cam‐Clay model. This leads to a new method of predicting the stress‐strain response along such paths. The input parameters can be determined from constant σ3 tests and constant principal‐stress ratio tests. Excellent agreement with test results is achieved.

A normalizing relation for granular materials

It is hypothesized that a normalized shear stress – strain curve for granular materials can be obtained by accounting fully for the effects of volume change. In this sense, volume change behavior is a factor that controls the shear stress – strain behavior of a granular material. This hypothesis is applied to Rowe's stress-dilatancy theory to include slip, rolling, rearrangement, and crushing strains, and a theoretical normalizing relation is obtained. The relation is demonstrated to be reasonably correct for the published test data utilized in this study. Differing fabrics of a granular material at the same void ratio can be corrected for by the normalizing relation. The hypothesis is also applied to simple shear behavior and an empirical normalizing relation is obtained.On the basis of the success of the normalizing relation, it is suggested that the volume change rate at 4% axial strain may be, in relation to shear behavior, a more appropriate characterizing parameter than void ratio. However, owing to the long-standing use and acceptance of void ratio, the concept of a reference void ratio, determined by specific sample preparation and testing procedures, is introduced as a characterizing parameter for granular materials. Key words: volume change, dilatancy, normalization, fabric, stress, strain, deformation, sand, granular material.