A critical-state constitutive model for liquefiable sand

2005 ◽  
Vol 42 (3) ◽  
pp. 830-855 ◽  
Author(s):  
SM Reza Imam ◽  
Norbert R Morgenstern ◽  
Peter K Robertson ◽  
David H Chan
Keyword(s):  
Constitutive Model ◽  
Critical State ◽  
Stress Ratio ◽  
Large Strain ◽  
Triaxial Compression ◽  
Loose Sand ◽  
Inherent Anisotropy ◽  
Dense Sand ◽  
Peak Point ◽  
Wide Range

This paper presents a critical-state constitutive model for sands over a wide range of void ratios and consolidation pressures in a triaxial plane. A single set of parameters, including a unique critical-state line reached at large strain, is also used in the model, and differences in behavior in triaxial compression and extension are modeled by accounting for anisotropy at small and medium ranges of strain. The model uses a capped yield surface (YS), which is characterized by its size and shape. Following evidence in past literature, the stress ratio at the peak point of the capped YS of loose sands is approximated by the stress ratio measured at the peak point of their undrained effective stress path. Yielding parameters obtained using this stress ratio are also applied in modeling dense sand behavior and drained loading. These parameters account for the effects of inherent anisotropy, void ratio, and confining pressure on yielding stresses and are readily determined from laboratory tests, but further research is required on their determination from field data. The model accounts for stress-induced and inherent anisotropies, using different parameters, which develop and evolve independently. Emphasis is placed on proper modeling of aspects of loose sand behavior that affect their susceptibility to flow liquefaction.Key words: constitutive modeling, liquefaction, loose sand, critical state, dilatancy, hardening.

Stress–dilatancy in very loose sand

2004 ◽  
Vol 41 (5) ◽  
pp. 972-989 ◽  
Author(s):  
Ken Been ◽  
Michael Jefferies
Keyword(s):  
Stress Ratio ◽  
Triaxial Compression ◽  
Constitutive Relations ◽  
Soil Liquefaction ◽  
Fundamental Aspect ◽  
Triaxial Tests ◽  
Loose Sand ◽  
Dense Sand ◽  
Stress Criterion ◽  
Undrained Strength

Virtually all investigation of liquefaction has used undrained tests, and it has become common to represent the undrained strength in terms of a collapse surface or collapse stress ratio described by an effective friction angle. A difficulty with undrained tests is that they only allow observation of the interaction of elastic and plastic strain because of the imposed boundary condition (i.e., no drainage or zero volume change), precluding a proper understanding of an effective stress criterion for maximum undrained strength. Drained triaxial tests do not suffer from this shortcoming, and stress–dilatancy of dense sands in drained shear is well established as a fundamental aspect of sand behaviour, based on micromechanical considerations. It is particularly interesting to consider the stress–dilatancy behaviour of very loose sands in the context of soil liquefaction. Although there are some data in the literature on loose sand behaviour in drained triaxial compression, the majority of data are actually for sands markedly denser than sands showing static liquefaction in undrained tests. This paper therefore reports some laboratory testing of very loose sands, together with comparative undrained liquefaction data, and compares the loose behaviour to that of dense sand. These data are reduced to stress–dilatancy form so that the fundamental aspects of loose soil behaviour can be seen and compared to flow rules used in constitutive models. The stress–dilatancy of very loose sand shows no limiting stress ratio markedly less than that of the critical state. Moreover, the stress–dilatancy trends of very loose sand are the same as those of dense sand. There is no evidence of "structural collapse" of the particulate arrangement of very loose sands, contrary to speculation associated with collapse surfaces in the literature. Explanations of sand liquefaction must seek other physical explanations of the soil behaviour.Key words: sand, constitutive relations, plasticity, liquefaction.

Measurement and Calibration of the Parameters of Hypoplasticity Model for an Iraqi Soil

2020 ◽  
Vol 857 ◽  
pp. 243-252
Author(s):  
Aysar Hassan Subair ◽  
Ala Nasir Aljorany
Keyword(s):  
Constitutive Model ◽  
Void Ratio ◽  
Initial Stresses ◽  
Model Parameters ◽  
State Variables ◽  
Soil Behavior ◽  
Dense Sand ◽  
Hypoplastic Model ◽  
Material Parameters ◽  
Wide Range

There are many constitutive models that have been used to model the mechanical behavior of soils. Some of these models are either unable to represent important features such as the strain softening of dense sand or required many parameters that can be hard to obtain by standard laboratory tests. Because of that, a more reliable constitutive model, which is capable to capture the main features of the soil behavior with easily obtained parameters, is required. The Hypoplasticity model is considered as a promising constitutive model in this respect. It is considered as a particular class of rate non-linear constitutive model at which the stress increment is expressed in a tensorial equation as a function of strain increment, actual stress, and void ratio. The hypoplastic model required only eight material parameters (critical friction angle critical, maximum and minimum void ratio respectively), granular stiffness hs and the model constants n, α, β). The appealing feature of the hypoplastic model is that the material parameters are separated from the state variables (void ratio and the initial stresses). This feature enables the model to simulate the soil behavior under a wide range of stresses and densities with the same set of material parameters. In this research, a brief description of the Hypoplasticity model is presented. Detailed discussions regarding the measurement and calibration of the model parameters of an Iraqi soil are then exposed. It is concluded that only Consolidated Drained (CD) triaxial test, oedometer test, and the well-known limit density tests are needed to get all the parameters of the hypoplasticity model.

scholarly journals Stress–Dilatancy Relationship of Erksak Sand under Drained Triaxial Compression

Geosciences ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 353
Author(s):  
Katarzyna Dołżyk-Szypcio
Keyword(s):  
Stress Ratio ◽  
Triaxial Compression ◽  
Stable Condition ◽  
Compression Tests ◽  
Ultimate State ◽  
Dense Sand ◽  
The One ◽  
Two Parameters ◽  
Relationship Of ◽  
Triaxial Compression Tests

Analyzing the results of triaxial compression tests under drained conditions for Erksak sand published in the literature, the stress–dilatancy relationships were described using the frictional state concept. At all phases of shearing, the linear stress ratio–plastic dilatancy relationship can be expressed by the critical frictional state angle and two parameters of the frictional state concept. At failure, dense sand exhibits purely frictional behavior (α = 0, β = 1) and the stress ratio–dilatancy relationship may be correctly described by the Rowe, Bolton, and frictional state concept relationships. Very loose Erksak sand sheared under drained triaxial compression at the ultimate state reaches a stable condition, but the reached stress ratio is significantly smaller than the one at a critical state.

scholarly journals Large-Strain Hyperelastic Constitutive Model of Envelope Material under Biaxial Tension with Different Stress Ratios

Materials ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 1780 ◽  
Author(s):  
Zhipeng Qu ◽  
Wei He ◽  
Mingyun Lv ◽  
Houdi Xiao
Keyword(s):  
Constitutive Model ◽  
Stress Ratio ◽  
Biaxial Tension ◽  
Large Strain ◽  
Tensile Failure ◽  
Biaxial Tensile ◽  
Envelope Material ◽  
Fiber Matrix ◽  
Stress Ratios ◽  
Fiber Interaction

This paper reports the biaxial tensile mechanical properties of the envelope material through experimental and constitutive models. First, the biaxial tensile failure tests of the envelope material with different stress ratio in warp and weft directions are carried out. Then, based on fiber-reinforced continuum mechanics theory, an anisotropic hyperelastic constitutive model on envelope material with different stress ratio is developed. A strain energy function that characterizes the anisotropic behavior of the envelope material is decomposed into three parts: fiber, matrix and fiber–fiber interaction. The fiber–matrix interaction is eliminated in this model. A new simple model for fiber–fiber interaction with different stress ratio is developed. Finally, the results show that the constitutive model has a good agreement with the experiment results. The results can be used to provide a reference for structural design of envelope material.

Laboratory Testing and Consitiutive Modeling of Coal Including Anisotropy

1992 ◽  
Vol 296 ◽  
Author(s):  
Dar-Hao Chen ◽  
Musharraf M. Zaman ◽  
Anant R. Kukreti
Keyword(s):  
Constitutive Model ◽  
Triaxial Compression ◽  
High Capacity ◽  
Ground Surface ◽  
Transversely Isotropic ◽  
Confining Pressure ◽  
Inherent Anisotropy ◽  
Deformation Response ◽  
Young’S Moduli ◽  
Confining Pressures

AbstractIn this study, the stress-deformation response of coal in the laboratory under threedimensional (3-D) loading conditions similar to those existing in an actual coal mine is investigated, and a constitutive model, including the effects of anisotropy, is developed. The coal samples were obtained from a mine in LeFlore County, Oklahoma, at a depth of approximately 25–30 ft below the ground surface. A High Capacity Cubical Device with servo-controlled independent loading along three axes of a cubical specimen and a computerized data acquisition and monitoring system were used to conduct the tests. A total of 21 tests under 4 different confining pressures and 5 different stress paths were conducted. The influence of the degree of anisotropy was investigated by comparing the transversely isotropic and isotropic idealizations for different stress paths (Triaxial Compression, Triaxial Extension and Simple Shear) at different confining pressures (1,600, 3,200 and 5,600 psi). The experimental results demonstrated that the coal exhibits inherent anisotropy and that it can be treated approximately as a transversely isotropic material. Also, the Young's moduli were found to be dependent on the confining pressure. The experimental data were used to evaluate the material constants associated with the elasto-plastic constitutive model developed in the study.

Uniaxial Ratchetting of 316FR Steel at Room Temperature— Part II: Constitutive Modeling and Simulation

1998 ◽  
Vol 122 (1) ◽  
pp. 35-41 ◽  
Author(s):  
N. Ohno ◽  
M. Abdel-Karim
Keyword(s):  
Constitutive Model ◽  
Constitutive Modeling ◽  
Critical State ◽  
Room Temperature ◽  
Stress Ratio ◽  
Dynamic Recovery ◽  
Kinematic Hardening ◽  
Hysteresis Loops ◽  
Hardening Model ◽  
Stress Cycling

Uniaxial ratchetting experiments of 316FR steel at room temperature reported in Part I are simulated using a new kinematic hardening model which has two kinds of dynamic recovery terms. The model, which features the capability of simulating slight opening of stress-strain hysteresis loops robustly, is formulated by furnishing the Armstrong and Frederick model with the critical state of dynamic recovery introduced by Ohno and Wang (1993). The model is then combined with a viscoplastic equation, and the resulting constitutive model is applied successfully to simulating the experiments. It is shown that for ratchetting under stress cycling with negative stress ratio, viscoplasticity and slight opening of hysteresis loops are effective mainly in early and subsequent cycles, respectively, whereas for ratchetting under zero-to-tension only viscoplasticity is effective. [S0094-4289(00)00501-6]

Undrained anisotropy of Hostun RF loose sand: new experimental investigations

2006 ◽  
Vol 43 (11) ◽  
pp. 1195-1212 ◽  
Author(s):  
Zeina Finge ◽  
Thiep Doanh ◽  
Phillippe Dubujet
Keyword(s):  
Effective Stress ◽  
Stress Ratio ◽  
Triaxial Compression ◽  
Stress Path ◽  
Experimental Investigations ◽  
Loose Sand ◽  
Induced Anisotropy ◽  
Static Liquefaction ◽  
Stress States ◽  
Effective Stress Ratio

The undrained behaviour of loose and overconsolidated Hostun RF sand in triaxial compression and extension tests is described. The samples are isotropically or anisotropically overconsolidated along several constant effective stress ratio paths with various overconsolidation ratios (OCR), up to 24. To minimize the effect of variation of density on the observed undrained behaviour, all tested samples are required to have a nearly identical void ratio before the final monotonic undrained shearing. Isotropically overconsolidated and normally consolidated samples exhibit the same phenomenon of partial static liquefaction, but anisotropically overconsolidated specimens reveal a completely different undrained behaviour. A common pseudoelastic response is observed for a given overconsolidation history. This response is induced by recent stress history in terms of effective stress paths, independent of the OCR during overconsolidation. The initial gradient of the effective stress paths seems to depend solely on the direction of the previous linear stress path history. This paper offers a comprehensive understanding of the mechanism of the induced anisotropy of loose sand created by simple linear stress paths from three different initial stress states in the classical triaxial plane. The pseudoelastic response can be adequately modelled by a simple hyperelastic component of the elastoplastic framework.Key words: induced anisotropy, overconsolidation, instability, laboratory undrained tests, sand, hyperelasticity.

Experimental observations on the response of loose sand under simultaneous increase in stress ratio and rotation of principal stresses

2008 ◽  
Vol 45 (5) ◽  
pp. 597-610 ◽  
Author(s):  
Dharma Wijewickreme ◽  
Yoginder P. Vaid
Keyword(s):  
Principal Stress ◽  
Stress Ratio ◽  
Shear Stiffness ◽  
Stress Path ◽  
Simultaneous Increase ◽  
Loose Sand ◽  
Horizontal Shear ◽  
Principal Stresses ◽  
Inherent Anisotropy ◽  
Strain Paths

The drained response of loose sand (relative density of 30%) under simultaneous increase in principal stress ratio (R = σ'1/σ'3) and the inclination of major principal stress to the vertical (ασ) is examined using data from hollow cylinder torsional shear testing. The study specifically pertains to the behaviour of loose sand subject to monotonic linear stress path loadings in the R–ασ space, within the domain of R ≤ 2, ασ < 45°, while intermediate principal stress parameter (b) and effective mean normal stress (σ'm) are held constant. The relationship between horizontal shear stress (τzt) and horizontal shear strain (γzt) of loose sand under such loadings is shown to be unique and stress-path independent. At any stress state, the horizontal shear stiffness (dτzt/dγzt) for a given σ'm depends only on the current value of τzt, and not on the value of individual components of normal effective stress, or their increments. When R and ασ are increased simultaneously in a linear manner, loose sand initially exhibits linear strain paths, suggesting no significant changes to the inherent anisotropy during the early stages of such loading. The directions of principal stress increment (αΔσ) and principal strain increment (αΔε) are found coincident, when αΔσ < 45°. An approach to predict the response of loose sand under simultaneous increase in R and ασ with constant b and σ'm has been developed based on these findings.

scholarly journals Study on Damage Constitutive Model of Rock under Freeze-Thaw-Confining Pressure-Acid Erosion

2021 ◽  
Vol 11 (20) ◽  
pp. 9431
Author(s):  
Youliang Chen ◽  
Peng Xiao ◽  
Xi Du ◽  
Suran Wang ◽  
Tomas Manuel Fernandez-Steeger ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Damage Evolution ◽  
Damage Mechanics ◽  
Triaxial Compression ◽  
Confining Pressure ◽  
Model Parameters ◽  
Theoretical Derivation ◽  
Freeze Thaw ◽  
Peak Point ◽  
Damage Constitutive Model

Aiming at the acid-etched freeze-thaw rock for geotechnical engineering in cold regions, chemical damage variables, freeze-thaw damage variables, and force damage variables were introduced to define the degree of degradation of rock materials, the law of damage evolution, the total damage variable of acid-corroded rock under the coupling action of freeze-thaw and confining pressure was deduced. The continuous damage mechanics theory was adopted to derive the damage evolution equation and constitutive model of acid-eroded rock under the coupling action of freeze-thaw and confining pressure. The theoretical derivation method was used to obtain the required model parameter expressions. Finally, the model’s rationality and accuracy were verified by the triaxial compression test data of frozen-thawed rocks. Comparing the test curve’s peak point with the peak point of the model theoretical curve, the results show that the two are in suitable agreement. The damage constitutive model can better reflect the stress-strain peak characteristics of rock during triaxial compression, verifying the rationality and reliability of the model and the method for determining the model parameters. The model extends the damage model of rock under the coupling action of freeze-thaw and confining pressure in the chemical environment and further reveals the damage mechanism and failure law of acid-corroded rock under the coupling action of freeze-thaw and confining pressure.

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