An elasto-plastic constitutive model for soft rock with strain softening

1995 ◽  
Vol 19 (4) ◽  
pp. 233-247 ◽  
Author(s):  
T. Adachi ◽  
F. Oka
Keyword(s):  
Constitutive Model ◽  
Strain Softening ◽  
Soft Rock

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.

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.

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

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.

scholarly journals Elastoplastic Analysis of Circular Opening Based on a New Strain-Softening Constitutive Model and Its Engineering Application in Hydraulic Fracturing

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
T. Yang ◽  
Q. S. Ye
Keyword(s):  
Rock Mass ◽  
Constitutive Model ◽  
Hydraulic Fracturing ◽  
Bearing Capacity ◽  
Fracture Zone ◽  
Strain Softening ◽  
Circular Opening ◽  
Elastic Peak ◽  
Load Bearing ◽  
Plastic Model

Constitutive effect is extremely important for the research of the mechanical behavior of surrounding rock in hydraulic fracturing engineering. In this paper, based on the triaxial test results, a new elastic-peak plastic-softening-fracture constitutive model (EPSFM) is proposed by considering the plastic bearing behavior of the rock mass. Then, the closed-form solution of a circular opening is deduced with the nonassociated flow rule under the cavity expansion state. Meanwhile, the parameters of the load-bearing coefficient and brittles coefficient are introduced to describe the plastic bearing capacity and strain-softening degrees of rock masses. When the above two parameters take different values, the new solution of EPSFM can be transformed into a series of traditional solutions obtained based on the elastic-perfectly plastic model (EPM), elastic-brittle plastic model (EBM), elastic-strain-softening model (ESM), and elastic-peak plastic-brittle plastic model (EPBM). Therefore, it can be applied to a wider range of rock masses. In addition, the correctness of the solution is validated by comparing with the traditional solutions. The effect of constitutive relation and parameters on the mechanical response of rock mass is also discussed in detail. The research results show that the fracture zone radii of circular opening presents the characteristic of EBM > EPBM > ESM > EPSFM; otherwise, it is on the contrast for the critical hydraulic pressure at the softening-fracture zone interface; the postpeak failure radii show a linear decrease with the increase of load-bearing coefficients or a nonlinear increase with the increasing brittleness coefficient. This study indicates that the rock mass with a certain plastic bearing capacity is more difficult to be cracked by hydraulic fracturing; the higher the strain-softening degree of rock mass is, the easier it is to be cracked. From a practical point of view, it provides very important theoretical values for determining the fracture range of the borehole and providing a design value of the minimum pumping pressure in hydraulic fracturing engineering.

Stury of Post-Failure Constitutive Relation Based on SMP Criterion

2013 ◽  
Vol 790 ◽  
pp. 405-409
Author(s):  
Jian Ming Zhu ◽  
Ze Xiang Wu ◽  
Qi Zhao ◽  
Chong Yang
Keyword(s):  
Residual Stress ◽  
Elastic Modulus ◽  
Constitutive Model ◽  
Constitutive Relation ◽  
Strain Softening ◽  
Friction Angle ◽  
Peak Friction Angle ◽  
Confining Pressures ◽  
Intermediate Variables ◽  
Nonlinear Elastic

In this paper, based on SMP criteria, combination of strain softening of rock material mechanics theory, the after peak friction angleφfor the intermediate variables, the residual strainεto express the after peak nonlinear elastic modulusE, and finally establish a unified non-linear constitutive model of the rock peak residual stress. Combination Xiao Guanzhuang Eastern Mine typical breakdown rock of diorite triaxial test , get stress-strain curves for different confining pressures by this model. It shows that peak constitutive relation of this study can simulate the experimental results, prove the rationality of the model.

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