scholarly journals An Elastoplastic Strain-Hardening and Strain-Softening Constitutive Model for Soft Rock Considering the Influence of Intermediate Stress

2003 ◽  
Vol 43 (5) ◽  
pp. 107-117 ◽  
Author(s):  
Feng Zhang ◽  
Atsushi Yashima ◽  
Guang Lin Ye ◽  
Toshihisa Adachi ◽  
Fusao Oka
Keyword(s):  
Constitutive Model ◽  
Strain Hardening ◽  
Strain Softening ◽  
Soft Rock ◽  
Elastoplastic Strain

STUDY ON SOFTENING CONSTITUTIVE MODEL OF SOFT ROCK USING STRAIN SPACE BASED UNIFIED STRENGTH THEORY

2008 ◽  
Vol 22 (31n32) ◽  
pp. 5375-5380 ◽  
Author(s):  
LI SONG ◽  
CHONGDU CHO ◽  
SHENG LU ◽  
HONGJIAN LIAO
Keyword(s):  
Constitutive Model ◽  
Constitutive Equations ◽  
Strain Softening ◽  
Soft Rock ◽  
Elastoplastic Strain ◽  
Strength Theory ◽  
Unified Strength Theory ◽  
Softening Behavior ◽  
Simulation Results ◽  
Strain Space

This study attempts to modify the unified strength theory by considering compression as a positive load in geotechnical engineering. It also aims to establish a unified elastoplastic strain softening constitutive model which can accurately describe the strain softening behavior of one kind of soft rocks distributed in Japan. The hardening function parameters of the unified elastoplastic strain softening constitutive model are determined from experiments. In addition, numerical simulations of this model are performed to compare the pre-peak, post-peak and the residual strengths of soft rock predicted by this study and experimental results. Simulation results demonstrated that the proposed constitutive equations in strain space can well describe the softening behavior and accurately predict the peak and residual strengths of soft rock. While the proposed equation is applicative for normally consolidated state and overconsolidated state according to the simulation results.

Visco-Elastic-Plastic Constitutive Model for A7N01-T6 Alloy Welding and Analytical Solutions with Finite Element Codes

2013 ◽  
Vol 446-447 ◽  
pp. 284-287
Author(s):  
K.J. Song ◽  
Y.H. Wei ◽  
Z.B. Dong ◽  
K. Fang ◽  
W.J. Zheng ◽  
...  
Keyword(s):  
Finite Element ◽  
Plastic Strain ◽  
Constitutive Model ◽  
Strain Hardening ◽  
Strain Softening ◽  
Great Influence ◽  
Welding Process ◽  
Welding Residual Stress ◽  
Creep Equation ◽  
Maximum Deformation

This paper has established a viscoelasticplastic constitutive model for A7N01T6 alloy welding, which is temperature and deformation history dependent. The model uses elasticmixed hardening plastic and creep equation to describe the strain hardening at low temperatures and strain softening at high temperatures, respectively. Then it is applied for finite element numerical simulation of the welding process. By comparison with the conventional temperature dependent elasticperfectly plastic model, the overall longitudinal residual compressive plastic strain and the maximum deformation of welding sheet are larger. This is because that the plastic strain is mostly produced in high temperature range. Strain softening has great influence on the evolution of plastic strain. The compressive plastic strain during heating is larger than the tensile plastic strain during cooling. Strain hardening effect on welding residual strain and stress is almost negligible. Using the established constitutive model, welding residual stress and strain are in good agreement with the theoretical results.

Constitutive Model of Strain Softening for Soft Rock

2011 ◽  
Vol 250-253 ◽  
pp. 1932-1935
Author(s):  
Song Li ◽  
Hong Jian Liao ◽  
Hang Zhou Li
Keyword(s):  
Constitutive Model ◽  
Strain Softening ◽  
Three Dimensional ◽  
Soft Rock ◽  
Unified Strength Theory ◽  
Softening Behavior ◽  
Proposed Model ◽  
Deviatoric Plane ◽  
Modified Equation ◽  
Rock Specimens

This paper aims to study the strain softening behavior of soft rock. A modified equation of unified strength theory is proposed that is convenient to be applied in geotechnical engineering where compression is customarily taken as positive. And also the limit line on deviatoric plane of this modified equation is derived and introduced into the three dimensional (3D) elastic viscoplastic constitutive model of Yin and Graham. Parameters of the model are determined from experiments of the diatom soft rock specimens. Numerical simulations are performed to compare the strain softening behavior predicted in this paper and triaxial experimental results. Simulation results show that the proposed model can accurately describe the strain softening of soft rock.

scholarly journals Effect of Intermediate Principal Stress on the Bearing Capacity of Footings in Soft Rock

Coatings ◽  
2021 ◽  
Vol 11 (9) ◽  
pp. 1019
Author(s):  
Zongyuan Ma ◽  
Faning Dang ◽  
Hongjian Liao
Keyword(s):  
Constitutive Model ◽  
Bearing Capacity ◽  
Strain Hardening ◽  
Principal Stress ◽  
Numerical Solutions ◽  
Soft Rock ◽  
Intermediate Principal Stress ◽  
Rock Foundation ◽  
Unified Strength Theory ◽  
Bearing Capacity Factor

The bearing capacity for footings is a fundamental scientific problem in civil engineering. The evaluation of the bearing capacity of footings usually does not take into account the effect of the intermediate principal stress. In practice, the intermediate principal stress has certain influences on the strength of geomaterials (e.g., rock and soil) or concrete. In this paper, a series of numerical solutions are presented to evaluate the bearing capacity of footings in a soft rock foundation via a two-dimensional finite difference code (FLAC) with a strain hardening/softening constitutive model based on the unified strength theory (UST). The values of the bearing capacity factor Nc and Nγ for strip, circular and square footings in a soft rock foundation were evaluated using the strain hardening/softening constitutive model. The effect of the intermediate principal stress on the bearing capacity of strip, circular and square footings in a soft rock foundation was analyzed. The results of the numerical computation show that the intermediate principal stress has a significant influence on the bearing capacity and failure mechanisms of a soft rock medium. The influence of the intermediate principal stress on the peak and residual values of the bearing capacity for a strip footing is much greater than for circular and square footings. Research works for the reasonable estimation of the bearing capacity of footings in soft rock are facilitated by this study.

scholarly journals Assessment of the mechanism of fracture propagation of soft rock coastal cliffs by using non-local constitutive models

2020 ◽  
Author(s):  
Piernicola Lollino ◽  
Nunzio Luciano Fazio ◽  
Michele Perrotti ◽  
Alessio Genco ◽  
Gaetano Elia ◽  
...  
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Strain Softening ◽  
Strong Dependence ◽  
Fracture Propagation ◽  
Soft Rock ◽  
Numerical Results ◽  
Regularization Techniques ◽  
Coastal Cliffs ◽  
Non Local

<p>The assessment of susceptibility to failure of soft rock coastal cliffs, along with the associated failure mechanism, is not a simple task. Equilibrium conditions depend on the combination of several factors such as structural setting, rock mechanical strength, weathering processes, the hydro-mechanical action of sea waves, the variation of the rock cliff geometry, to mention some of the most important ones. From a geomechanical perspective, the brittle - strain softening behaviour of the rocks plays a key role in the onset and propagation of failure (Ciantia & Castellanza 2015). In particular, the rapid strength reduction occurring after peak under mechanical loading leading to localised deformations within shear fractures is detrimental for rock cliffs. Taking rock brittleness into account in numerical simulations under the framework of continuum mechanics is not straightforward, due to the problems related to a strong dependence of the numerical results from the adopted mesh when strain-softening laws are implemented (Vermeer and Brinkgreve 1994). Nowadays, several regularization techniques are available to control the size of the localised region and prevent the mesh dependence. Within regularization techniques, the nonlocal integral type solution has the advantage of not changing the field equations which facilitates numerical implementation. In this approach, the chosen nonlocal variables are valuated from spatial averages of the field variables in a neighbourhood, and the constitutive model is updated by replacing a local variable with its nonlocal counterpart. Consequently, the constitutive response of a Gauss point is influenced by all the integration points within a neighbourhood, with the size determined through a characteristic length (Bažant and Jirásek 2002). This contribution addresses the problem of the stability of an ideal 2-D plane strain coastal cliff, 20-m high, by means of the use of a non-local constitutive model implemented in a commercial finite element code (Mánica et al. 2018). The numerical results show insights into the evolution of the strain field and the process of slip surface/fracture propagation in the rock cliff as well as highlight the importance of regularising the finite element solution in the presence of brittle materials.</p>

Numerical Modeling of the Constitutive Relationship of a Soft Rock Using a 3-D Elastic Visco-Plastic Model

2004 ◽  
Vol 261-263 ◽  
pp. 723-728
Author(s):  
Li Jun Su ◽  
Hong Jian Liao ◽  
Jian Hua Yin
Keyword(s):  
Constitutive Model ◽  
Strain Softening ◽  
Soft Rock ◽  
Time Dependent ◽  
Triaxial Tests ◽  
Flow Rule ◽  
Test Results ◽  
Stress Strain ◽  
Strain Behavior ◽  
Constitutive Formulation

In this paper, a diatomaceous soft rock is studied. Triaxial tests had been conducted on this soft rock. From the test results, it is found that the stress-strain curve of this soft rock has a notable strain-softening tendency. In order to study its time-dependent stress-strain behavior, a constitutive model that can describe not only the strain-hardening behavior, but also the strain-softening behavior must be constructed. Based on Perzyna’s fundamental assumptions of the elastic visco-palstic theory, a visco-plastic flow rule, and Yin and Graham’s 3-D elastic visco-palstic constitutive model (3-D EVP model), the constitutive formulation under a triaxial stress state is obtained in this paper. The derived formulation can be used to simulate the time-dependent stress-strain behavior of both consolidated undrained and consolidated drained triaxial tests of soils and rocks. In this paper, the constitutive formulation is used to simulate the time-dependent stress-strain behavior of consolidated undrained triaxial tests of the soft rock studied in this paper. The simulated results are compared with the triaxial test results. The comparison of the results shows that model predictions agree well with measured results. This demonstrates that the EVP model can be used to describe the time-dependent stress-strain behavior of the soft rock studied in this paper.

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