A Constitutive Model of Sandstone Considering the Post Peak Behavior

2017 ◽  
Vol 35 (1) ◽  
pp. 13-25 ◽  
Author(s):  
F. S. Jeng ◽  
M. C. Weng ◽  
F. H. Yeh ◽  
Y. H. Yang ◽  
T. H. Huang
Keyword(s):  
Constitutive Model ◽  
Nonlinear Elasticity ◽  
Strain Curve ◽  
Shear Loading ◽  
Triaxial Tests ◽  
Flow Rule ◽  
Plastic Behavior ◽  
Softening Behavior ◽  
Proposed Model ◽  
Confining Pressures

AbstractIn rock engineering, evaluating the post-peak strength and deformation of rock is necessary. To explore the elasto-plastic behavior of sandstone in the post-peak stage, a series of strain-controlled triaxial tests were conducted under different confining pressures. According to the post-peak characteristics, a constitutive model based on nonlinear elasticity and generalized plasticity is proposed. This proposed model is characterized by the following features: (1) Nonlinear elasticity is observed under hydrostatic and shear loading; (2) the associated flow rule is followed; (3) substantial plastic deformation occurs during shear loading; and (4) post-peak softening behavior is accurately predicted. This model requires twelve material parameters, three for elasticity and nine for plasticity. The proposed model was validated by comparing the triaxial test results of Mushan sandstone at different hydrostatic pressures under dry and saturated conditions. In addition, the model is versatile; it can simulate the deformational behavior of two other sandstones. In summary, the proposed model can reasonably predict the complete stress–strain curve of sandstone.

A Characteristic and a Precisely Constitutive Model for Undrained Clay

2020 ◽  
Vol 975 ◽  
pp. 203-207
Author(s):  
Shih Tsung Hsu ◽  
Wen Chi Hu ◽  
Yu Heng Lin ◽  
Zhuo Ling
Keyword(s):  
Shear Strength ◽  
Plastic Strain ◽  
Constitutive Model ◽  
Strain Hardening ◽  
Undrained Shear Strength ◽  
Triaxial Tests ◽  
Stress Strain ◽  
Proposed Model ◽  
Taipei Basin ◽  
Undrained Shear

Constitutive models for soils are usually adopted in numerical method to analyze the behavior of geotechnical structures. This study performs a series of consolidated-undrained triaxial tests to establish the stress-strain curve of clay. A constitutive model that considers continuous strain hardening-softening is proposed based on the results of triaxial tests. Triaxial test results reveal that undrained shear strength linearly increases with an increase in consolidated pressure , the normalized undrained shear strength is about 0.52 not only for this study but also for the other two cases around Taipei Basin. Due to undrained condition, an associated flow rule between plastic strain increment and stress tensor is adopted. As accumulative plastic strain or/and consolidated pressure change, the mobilized undrained shear strength also changes. All parameters needed for the proposed model can be expressed as a function of undrained shear strength Su, The mobilized undrained shear strength for the proposed model during strain hardening-softening can be in term of accumulative plastic strain. This model can calculate the stress-strain curves of clayed soils accurately.

scholarly journals Experimental study on the thermal damage characteristics of cement stone

2020 ◽  
pp. 317-317
Author(s):  
Feng Xu ◽  
Bowen Qian ◽  
Ling Tan ◽  
Jianqiang Xu ◽  
Shengchuan Tang ◽  
...  
Keyword(s):  
Strain Curve ◽  
Horizontal Wells ◽  
Friction Angle ◽  
Confining Pressure ◽  
Triaxial Tests ◽  
Cement Stone ◽  
Different Temperatures ◽  
Confining Pressures ◽  
Southwest Region ◽  
Sealing Failure

Aiming at the problem of cement ring sealing failure during deep high-temperature shale gas exploitation, comprehensively considering the influence of the characteristics of multi-cluster fracturing of multiple horizontal wells and formation temperature, the cementing cement the southwest region is taken as the research object. After exposure to different temperatures (95?C and 135?C) and for different times (5, 10 and 20 times), axial and triaxial tests with different confining pressures (0, 5 MPa, 15 MPa and 30 MPa) were carried out. The research shows that: (1) the stress-strain curve of cement stone after heat treatment can be divided into four stages: compaction, elastic, yield and post-peak stage. As the confining pressure increases, the compaction phase disappears, the yield phase increases, and we see the transition from brittle to ideal plasticity after the peak; (2) as the temperature and number of thermal cycles increase, the cohesive force decreases significantly, and the internal friction angle shows a slight increase. The elastic modulus and the peak strength decreased.

A constitutive model of concrete confined by steel reinforcements and steel jackets

2005 ◽  
Vol 32 (1) ◽  
pp. 279-288 ◽  
Author(s):  
Y-F Li ◽  
S-H Chen ◽  
K-C Chang ◽  
K-Y Liu
Keyword(s):  
Constitutive Model ◽  
Concrete Strength ◽  
Strain Curve ◽  
Steel Reinforcement ◽  
Confined Concrete ◽  
Stress Strain ◽  
Steel Jacket ◽  
Proposed Model ◽  
Concrete Cylinders ◽  
Different Types

In this paper, a total of 60 concrete cylinders 30 cm in diameter and 60 cm in length confined by steel jackets of different thicknesses and different types of lateral steel reinforcements are tested to obtain the stress–strain curves of the cylinders. A constitutive model is proposed to describe the behavior of concrete confined by steel reinforcement, steel jackets, and both steel reinforcement and steel jackets used to retrofit and strengthen reinforced concrete structures. The confined concrete stress–strain curve of the proposed model is divided into two regions: the curve in the first region is approximated using a second-order polynomial equation, and that in the second region using an nth-order power-law equation, where n is a function of the unconfined concrete strength and the lateral confining stress. The results of the experiments show that different types of lateral steel reinforcement contribute greatly to the compressive strength of concrete cylinders confined by the reinforcement. Comparing the stress–strain curves of the uniaxial test with that from the proposed model, we conclude that the proposed model for concrete confined by a steel jacket and lateral steel reinforcement can predict the experimental results very well.Key words: constitutive model, steel jacket, confined concrete.

scholarly journals Study of Damage Constitutive Model of Brittle Rocks considering Stress Dropping Characteristics

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Fei Li ◽  
Shuang You ◽  
Hongguang Ji ◽  
Hao Wang
Keyword(s):  
Constitutive Model ◽  
Triaxial Compression ◽  
Strain Curve ◽  
Brittle Rock ◽  
Model Parameters ◽  
Deformation And Failure ◽  
Brittle Rocks ◽  
Whole Process ◽  
Confining Pressures ◽  
Damage Constitutive Model

Deep brittle rock exhibits characteristics of rapid stress dropping rate and large stress dropping degree after peak failure. To simulate the whole process of deformation and failure of the deep brittle rock under load, the Lemaitre strain equivalent theory is modified to make the damaged part of the rock has residual stress. Based on the damage constitutive model considering residual strength characteristics, a correction factor reflecting stress dropping rate is added, the Weibull distribution is used to describe the inhomogeneity of rock materials, and Drucker–Prager criterion is used to quantitatively describe the influence of stress on damage; a damage constitutive model of deep brittle rock considering stress dropping characteristics is established. According to the geometric features of the rock stress-strain curve, the theoretical expressions of model parameters are derived. To verify the rationality of the model, triaxial compression experiments of deep brittle rock under different confining pressures are conducted. And the influence of model parameters on rock mechanical behaviour is analysed. The results show that the model reflects the stress dropping characteristics of deep brittle rock and the theoretical curve is in good agreement with the experimental results, which indicates that the proposed constitutive model is scientific and feasible.

A Simple Constitutive Model for Overconsolidated Clays

2011 ◽  
Vol 243-249 ◽  
pp. 2283-2286
Author(s):  
Yang Liu ◽  
Xian De Zhu ◽  
Zhi Gong
Keyword(s):  
Constitutive Model ◽  
Soil Mechanics ◽  
Flow Rule ◽  
Hardening Law ◽  
Proposed Model ◽  
Overconsolidated Clays ◽  
Strain Relationship ◽  
As Stress ◽  
Associated Flow Rule ◽  
Cam Clay

In the framework of critical state soil mechanics, a simple constitutive model for overconsolidated clays is proposed based on subloading surface and normal consolidation yield surface. A more rational hardening law is used to describe the change between subloading surface and the normal consolidation surface with plastic deformation and an associated flow rule is adopted. The model can describe many characteristics of overcaonsolidated clays, such as stress-strain relationship, strain hardening and softening, and stress dilatancy. Compared with the Cam-clay model, two more parameters are required which represents specific physical meanings. Numerical simulation is compared with data from triaxial drained compression test, indicating that the proposed model can rationally describe overconsolidated properties.

scholarly journals A Constitutive Model for Saturated Gravelly Sand Based on Higher-Order Dilatancy Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Dongjie Zhang ◽  
Fei Luo ◽  
Zhanyuan Zhu ◽  
Bin Luo ◽  
Jing Li ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Constitutive Model ◽  
Strain Hardening ◽  
Stress Path ◽  
Test System ◽  
Higher Order ◽  
Volume Shrinkage ◽  
Proposed Model ◽  
Comparison Results ◽  
Confining Pressures

A standard stress path triaxial test system was applied to carry out conventional triaxial shearing tests for gravelly sands under confining pressures ranging from 50 kPa to 400 kPa at the initial relative densities of 0.15, 0.35, 0.55, and 0.75, respectively. The test results show that all the samples of gravelly sand present strain hardening and shear contraction during the process of shearing test. Additionally, gravelly sands are significantly affected by the initial relative density. The hardening degree of gravelly sand samples rises in line with increasing initial relative densities during shearing tests. When initial relative densities Dr are at 0.15 and 0.35, the volume shrinkage of samples decreases with the increasing confining pressures. Instead, when initial relative densities Dr are at 0.55 and 0.75, the volume shrinkage of samples increases with the growth of confining pressures. To describe these triaxial shearing mechanical properties of gravelly sands, a higher-order dilatancy equation was proposed based on the concept of a super yield surface. A constitutive model which can describe the mechanical properties of gravelly sand was established when the associated flow laws were applied to compare with the results of the triaxial shearing test under the consolidated drained condition. The comparison results showed that the proposed model can reflect the strain hardening and shear contraction characteristics of gravelly sands from low to high confining pressures under different initial relative densities.

scholarly journals Triaxial Test and Mechanical Analysis of Rock-Soil Aggregate Sampled from Natural Sliding Mass

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Shuling Huang ◽  
Xiuli Ding ◽  
Yuting Zhang ◽  
Wei Cheng
Keyword(s):  
Mechanical Behavior ◽  
Large Scale ◽  
Mechanical Response ◽  
Strain Curve ◽  
Friction Angle ◽  
Mechanical Analysis ◽  
Soil Aggregate ◽  
Hydropower Plant ◽  
Triaxial Tests ◽  
Confining Pressures

Rock-soil aggregate, as a specific geomaterial, exhibits complicated mechanical behavior. The rock-soil aggregate sampled from the deep layer of sliding mass at Jinpingzi area of Wudongde hydropower plant on Yangtze River is investigated to understand its mechanical behavior. Large-scale laboratory triaxial tests are conducted considering different gradations, stone contents and confining pressures. The results show that variation of stone content and gradation considerably affects the mechanical characteristics of rock-soil aggregate. Further, the influences of stone content, and gradation variation on stress-strain curve, Mohr-Coulomb criterion based shear strength parameters, Duncan-Chang model based deformation parameters, and internal friction angle are analyzed. A modified Rowe’s stress-dilatancy equation describing the mechanical response of rock-soil aggregate is then suggested.

scholarly journals A Constitutive Model of Sandy Gravel Soil under Large-Sized Loading/Unloading Triaxial Tests

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Pengfei Zhang ◽  
Han Liu ◽  
Zhentu Feng ◽  
Chaofeng Jia ◽  
Rui Zhou
Keyword(s):  
Constitutive Model ◽  
Large Scale ◽  
Confining Pressure ◽  
Peak Strength ◽  
Triaxial Tests ◽  
Model Parameters ◽  
Sandy Gravel ◽  
Cumulative Volume ◽  
Gravel Soil ◽  
Confining Pressures

Based on large-scale triaxial tests of sandy gravel materials, the strength and deformation characteristics under loading/unloading conditions are analyzed. At the same time, the applicability of the hyperbolic constitutive model to sandy gravel is studied using experimental data. The results indicate that sandy gravel under low confining pressures (0.2 and 0.4 MPa) shows a weak softening trend; the higher the confining pressure, the more obvious the hardening tendency (0.6 and 0.8 MPa) and the greater the peak strength. During unloading tests, strain softening occurs, and the peak strength increases with increasing confining pressure. During loading tests, dilatancy appears when the confining pressure is low (0.2 MPa). With increasing confining pressure (0.4, 0.6, and 0.8 MPa), the dilatancy trend gradually weakens, and the cumulative volume tric strain increases, which reflects the relevance of the stress paths. Through research, it is found that the hyperbolic constitutive model has good applicability to sandy gravel soils, and the corresponding model parameters are obtained.

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 A Cyclic Plasticity Model with Martensite Transformation for S30408 and Its Finite Element Implementation

2020 ◽  
Vol 10 (17) ◽  
pp. 6002
Author(s):  
Yanan Chen ◽  
Xiaohui Chen ◽  
Bingjun Gao ◽  
Xu Chen ◽  
Kai Zhang ◽  
...  
Keyword(s):  
Finite Element ◽  
Stainless Steel ◽  
Austenitic Stainless Steel ◽  
Constitutive Model ◽  
Numerical Algorithm ◽  
Kinematic Hardening ◽  
Cyclic Plasticity ◽  
Flow Rule ◽  
Proposed Model ◽  
Metastable Austenitic Stainless Steel

The ability of the constitutive model to simulate the ratcheting behavior of metastable austenitic stainless steel S30408 is significant to ensure the safety of the liquefied natural gas (LNG) semi-trailer tanks in the lightweight process of the inner containers. This is because the lightweight inner vessels often encounter cyclic stresses due to the road inertia loads together with high mean stresses due to internal pressures. In this study, we performed cryogenic uniaxial tension experiments and a series of ratcheting experiments to investigate the cyclic plasticity behavior of the metastable austenitic stainless steel S30408. Based on the Ohno-Wang II model, we proposed a new cyclic plasticity constitutive model with martensitic transformation, which relates the content of deformation-induced martensite with isotropic hardening and kinematic hardening. The ratcheting behaviors of S30408 were first simulated by the proposed model with the incremental loading method using MATLAB. The results showed that the model could reasonably predict the ratcheting behavior of S30408, and the evolution law of martensite content could well predict the content of deformation-induced martensite. Under the assumption of the von Mises yield criterion and normal plasticity flow rule, we developed a numerical algorithm of plastic strain with the proposed model to implement the finite element calculation of the model. Internal iteration in the numerical algorithm was implemented with the Euler backward method, which calculated the trial strain for each equilibrium iteration using the consistent tangent matrix. With a user subroutine, the proposed model was programmed into ANSYS for a user - executable version. By simulating the uniaxial ratcheting of a S30408 round bar, we found that the calculated results were in good agreement with the experimental results, which promises further applications in the design of structures, such as LNG semi-trailer tanks.

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