Failure Surface and Plastic Potential in Deviatoric Plane of Bangkok Clay

2012 ◽  
Vol 256-259 ◽  
pp. 256-260
Author(s):  
Wanwarang Ratananikom ◽  
Siam Yimsiri ◽  
Fumihiko Fukuda ◽  
Suched Likitlersuang
Keyword(s):  
Principal Stress ◽  
Constitutive Modeling ◽  
Failure Surface ◽  
Intermediate Principal Stress ◽  
Triaxial Tests ◽  
Flow Rule ◽  
Plastic Potential ◽  
Stress Directions ◽  
Deviatoric Plane ◽  
Associated Flow Rule

This paper presents an experimental investigation on the failure surface and plastic potential in deviatoric plane of Bangkok Clay. The results of torsional shear hollow cylinder and triaxial tests with various principal stress directions and magnitudes of intermediate principal stress on undisturbed Bangkok Clay specimens are presented. The obtained stress-strain behaviors assert clear evidences of anisotropic characteristics of Bangkok Clay. Both failure surface and plastic potential in deviatoric plane of Bangkok Clay are demonstrated as isotropic and of circular shape (Drucker-Prager type) which implies an associated flow rule. Concerning the behavior of Bangkok Clay found from this study, the discussions on the effects of employed constitutive modeling approach on the resulting numerical analysis are made.

scholarly journals A Framework for Versatile Shape of Yield Surfaces for Structured Aniso-tropic Soft Soils

2016 ◽  
Author(s):  
Nallathamby Sivasithamparam ◽  
Jorge Castro
Keyword(s):  
Yield Surface ◽  
Earth Pressure ◽  
Type Model ◽  
Flow Rule ◽  
Lateral Movement ◽  
Plastic Potential ◽  
Yield Surfaces ◽  
Anisotropic Clays ◽  
Associated Flow Rule ◽  
Cam Clay

A framework based on logarithmic contractancy is proposed to produce versatile shapes of yield surfaces for structured anisotropic clays. The recently proposed constitutive model (E-SCLAY1S) is an extension of existing model called S-CLAY1S, which is a Cam Clay type model that accounts for anisotropy and structure. A new parameter called contractancy parameter is introduced to control the shape of the yield surface as well as the plastic potential (as an associated flow rule is applied). This new parameter can be used to fit the coefficient of earth pressure at rest, the undrained shear strength or the stiffness under shearing stress paths predicted by the model. The model predicts the uniqueness of the critical state line and its slope is independent of the contractancy parameter. The effect of the shape of the yield surface was investigated on computed results of a benchmark embankment constructed on Bothkennar (Scotland) clay by employing the E-SCLAY1S model as a user-defined soil model into the PLAXIS finite element code. The results demonstrate that the contribution of the shape of yield surface (logarithmic contractancy parameter) have a relatively large effect on lateral movement of subsoil beneath the toe of the embankment compared to the settlement of subsoil at the centre of the embankment.

scholarly journals Development of a polyaxial platen for testing true triaxial behavior of rocks

2021 ◽  
Author(s):  
Prasoon Garg ◽  
Bhardwaj Pandit ◽  
Brijes Mishra ◽  
G.L. Sivakumar Babu
Keyword(s):  
Stress State ◽  
Principal Stress ◽  
Axial Stress ◽  
Intermediate Principal Stress ◽  
Intact Rock ◽  
Triaxial Stress ◽  
Triaxial Tests ◽  
True Triaxial ◽  
True Triaxial Tests

Mining at greater depths can lead to stress-induced failure, especially in areas of high horizontal in-situ stress. The induced stresses around the opening are known to be in a poly-axial stress state where, σ_1≠ σ_2≠ σ_3 with special case of σ_3= 0 and σ_1, σ_2 ≠ 0 at its boundary. The conventional triaxial testing does not represent the actual in-situ strength of the rock in regions of high horizontal stress, as it ignores the influence of intermediate principal stress (σ_2). The typical poly-axial testing (biaxial and true-triaxial tests) of intact rock mostly requires sophisticated and expensive loading systems. This study investigated the mechanical behavior of intact rock under a poly-axial stress state using a simple and cost-effective design. The apparatus consists of biaxial frame and a confining device. The biaxial frame has two platens that apply equal stress in both directions (σ_1=σ_2) on a 50.8 mm cubical specimen when placed inside the uniaxial loading device. The confining device performed separate biaxial tests under constant intermediate principal stress (σ_2 = constant) and true-triaxial tests when used along with the biaxial frame. This study then compared the failure modes and peak strength of Berea Sandstone specimens with other biaxial/triaxial devices to validate the design of the poly-axial apparatus. We also performed uniaxial tests on both standard cylindrical samples and prismatic specimen of different slenderness ratios. These tests provided a complete understanding of the failure mode transition from standard uniaxial compressive tests to triaxial stress conditions on cubical specimen. Additionally, this study determined best-fitted strength envelopes for biaxial and triaxial stress state. Based on regression analysis, we found a quadratic polynomial to be a good fit to biaxial strength envelope. For true-triaxial strength envelope, we found the 3D failure criterion by Nadai (1950) to be a good fit with R^2 of 0.964

scholarly journals The Behavior of a Coarse Granular Material under Complex Stress Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Yuefeng Zhou ◽  
Jiajun Pan ◽  
Zhanlin Cheng ◽  
Yongzhen Zuo
Keyword(s):  
Granular Material ◽  
Principal Stress ◽  
Stress Ratio ◽  
Intermediate Principal Stress ◽  
Friction Reduction ◽  
Western China ◽  
Triaxial Tests ◽  
Confining Stress ◽  
True Triaxial ◽  
Prediction Approach

In recent years, dozens of high rockfill dams are under construction or planning for hydropower exploration in western China. In dam construction, the mechanical behavior of coarse granular material greatly affects the compatible deformation of dam body. In this article, an indirect in situ density prediction approach for coarse granular material is firstly proposed to solve the technical obstacle on prediction of the material density in thick overburden layer of a dam site in southwest China. Adopting a self-developed large-scale true triaxial apparatus with a special friction-reduction technique, four series of true triaxial tests were then performed to investigate the behavior of a coarse granular material with a maximum particle diameter of 60 mm. Test results show that the peak strength of the material increases together with the increasing confining stress and the increasing intermediate principal stress ratio. The material dilatancy is restricted by both the confining stress and the intermediate principal stress ratio. With the increase in intermediate principal stress ratio, the internal friction angle increases firstly and then decreases slightly, but the slope of stress path reduces gradually. The tested peak states were compared with several well-known strength criteria under the framework of generalized stress, showing a good fitness with the Lade–Duncan criterion and underestimation by the Mohr–Coulomb criterion and the Matsuoka–Nakai criterion. The strength envelope in the π plane shrinks with the increasing confining stress.

scholarly journals Solution of Strain-Softening Surrounding Rock in Deep Tunnel Incorporating 3D Hoek-Brown Failure Criterion and Flow Rule

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Jin-feng Zou ◽  
Song-qing Zuo ◽  
Yuan Xu
Keyword(s):  
Principal Stress ◽  
Failure Criterion ◽  
Strain Softening ◽  
Numerical Procedure ◽  
Intermediate Principal Stress ◽  
Surrounding Rock ◽  
Flow Rule ◽  
Stress Equilibrium ◽  
Novel Approach ◽  
Dilatancy Effect

In order to investigate the influence of the intermediate principal stress on the stress and displacement of surrounding rock, a novel approach based on 3D Hoek-Brown (H-B) failure criterion was proposed. Taking the strain-softening characteristic of rock mass into account, the potential plastic zone is subdivided into a finite number of concentric annulus and a numerical procedure for calculating the stress and displacement of each annulus was presented. Strains were obtained based on the nonassociated and associated flow rule and 3D plastic potential function. Stresses were achieved by the stress equilibrium equation and generalized Hoek-Brown failure criterion. Using the proposed approach, we can get the solutions of the stress and displacement of the surrounding rock considering the intermediate principal stress. Moreover, the proposed approach was validated with the published results. Compared with the results based on generalized Hoek-Brown failure criterion, it is shown that the plastic radius calculated by 3D Hoek-Brown failure criterion is smaller than those solved by generalized H-B failure criterion, and the influences of dilatancy effect on the results based on the generalized H-B failure criterion are greater than those based on 3D H-B failure criterion. The displacements considering the nonassociated flow rule are smaller than those considering associated flow rules.

scholarly journals An Extension Failure Criterion for Brittle Rock

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Aizhong Lu ◽  
Ning Zhang ◽  
Guisen Zeng
Keyword(s):  
Principal Stress ◽  
Poisson’S Ratio ◽  
Compressive Strain ◽  
Strength Criterion ◽  
Maximum Principal Stress ◽  
Intermediate Principal Stress ◽  
Brittle Rock ◽  
Poisson's Ratio ◽  
Triaxial Tests ◽  
True Triaxial

Under the triaxial compressive state, the compressive strain is supposed to happen in the direction of the maximum principal stress, but tensile strain happens in the direction of the minimum principal stress. Moreover, as the intermediate principal stress is not too high, the corresponding strain can also be tensile. If the brittle rock is assumed as linear elastic in the prefailure stage, a new strength criterion based on the sum of the two tensile strains was presented. The new criterion considers the differences in mechanical parameters (i.e., elastic modulus and Poisson’s ratio) under tension and compression. The parameters of the criterion only include Poisson’s ratio and uniaxial strength. And the effect of the intermediate principal stress σ 2 can be reflected. Certain featured failure phenomenon of rock material can be explained well by the proposed criterion. The results of conventional and true triaxial tests can verify the criterion well. Finally, the criterion is compared with the Mohr–Coulomb and Drucker–Prager criteria.

Slope Stability Analysis Using Unified Strength Theory

2011 ◽  
Vol 137 ◽  
pp. 59-64
Author(s):  
Zong Yuan Ma ◽  
Hong Jian Liao ◽  
Mao Hong Yu
Keyword(s):  
Slope Stability ◽  
Plane Strain ◽  
Principal Stress ◽  
Stability Problem ◽  
Factor Of Safety ◽  
Intermediate Principal Stress ◽  
Flow Rule ◽  
Problem Analysis ◽  
Strength Theory ◽  
Unified Strength Theory

Numerical computations using finite difference method and unified strength theory are reported to analyze the slope stability problem. The Factor of safety of plane strain and axisymmetric slopes was calculated by strength reducing method, and the influences of intermediate principal stress on slope stability problem was analyzed. The associative and non-associative flow rule was taking into account in plane strain slope problem analysis. The intermediate principal stress has equivalent influences on slope stability problem under associative and non-associative flow rule. The Factor of safety of plane strain slope is lower than the axisymmetric situation. The influence of intermediate principal stress on slope stability under plane strain condition is heavier than axisymmetry.

scholarly journals Simulation of the micro Single Point Incremental forming process of very thin sheets

2021 ◽  
Author(s):  
Stéphanie Thuillet ◽  
Pierre-Yves Manach ◽  
Fabrice Richard ◽  
Sébastien Thibaud
Keyword(s):  
Incremental Forming ◽  
Single Point ◽  
Small Diameter ◽  
Flow Rule ◽  
Single Point Incremental Forming ◽  
Shear Tests ◽  
Forming Process ◽  
Punch Force ◽  
Plastic Potential ◽  
Associated Flow Rule

The purpose of this paper is to simulate a complex forming process with parameters identified from tensile and shear tests. An elastic-plastic model is retained which combines a Hill’s 1948 anisotropic criterion and plastic potential using a non-associated flow rule. Firstly, a mechanical characterization is made with homogenous tests like tensile and shear tests [1]. On the other hand a process of micro Single Point Incremental forming is simulated [2]. It consists in deforming a clamped blank using a hemispherical punch which has a small diameter compared to the blank dimensions. From a small-size sheet of 0.2 mm thick, a square-based pyramid is obtained incrementally, with a define height path and advanced speed, by a tool instrumented to measure the forming force, which deforms locally the material. It is shown that the non-associated flow plasticity model leads to a good agreement between experimental and numerical results for the evolution of the punch force during the process.

Application of Associated and Non-Associated Flow Metal Plasticity for F.S.S Sheet

2021 ◽  
Vol 406 ◽  
pp. 473-480
Author(s):  
Oualid Chahaoui ◽  
Houssem Soltani ◽  
Nadjoua Matougui
Keyword(s):  
Sheet Metal ◽  
Sheet Metal Forming ◽  
Metal Forming ◽  
Mechanical Anisotropy ◽  
Flow Rule ◽  
Plastic Behavior ◽  
Sheet Plane ◽  
Yield Criteria ◽  
Plastic Potential ◽  
Associated Flow Rule

In the last decade, several phenomenological yield criteria for anisotropic material has been proposed to improve the modeling predictions about sheet metal-forming processes. In regard to this engineering application, two proprieties of models have been used. If the yield function and the plastic potential are not same (not equal), the normality rule is non associative flow rule (NAFR), otherwise, when the stresses yield has been completely coupled to the anisotropic strain rate ratio (plastic potential), is called the associated flow rule (AFR). The non-associated flow rule is largely adopted to predict a plastic behavior for metal forming, accurately about à strong mechanical anisotropy presents in sheet metal forming processes. However, various studies described the limits of the AFR concept in dealing with highly anisotropic materials. In this study, the quadratic Hill1948 yield criteria is considered to predict mechanical behavior under AFR and NAFR approach. Experiment and modeling predictions behaviour of normalized anisotropic coefficient r (θ) and σ (θ) evolved with θ in sheet plane. and the equibiaxial yield stress σb was assumed σb=1 but the rb-values was computed from Yld96 [15].

scholarly journals A Proposed Algorithm to Compute the Stress-Strain Plastic Region and Displacement of a Deep-Lying Tunnel Considering Intermediate Stress and Strain-Softening Behavior

2021 ◽  
Vol 12 (1) ◽  
pp. 85
Author(s):  
Jinwang Li ◽  
Xiufeng He ◽  
Caihua Shen ◽  
Xiangtian Zheng
Keyword(s):  
Principal Stress ◽  
Radial Displacement ◽  
Strain Softening ◽  
Plastic Region ◽  
Intermediate Principal Stress ◽  
Surrounding Rock ◽  
Parameter Analysis ◽  
Flow Rule ◽  
Stress Strain ◽  
Softening Behavior

Past studies on deep-lying tunnels under the assumption of plane strain have generally neglected the influence of intermediate principal stress even though this affects the surrounding rocks in the plastic zone. This study proposes a finite difference method to compute the stress strain plastic region and displacement of a tunnel based on the Drucker–Prager (D–P) yield criterion and non-associated flow rule and considering the influences of intermediate principal stress and the strain-softening behavior of surrounding rock. The computed results were compared with those of other well-known solutions and the accuracy and validity of the method were confirmed through some examples. Parameter analysis was conducted to investigate the effects of intermediate principal stress on stress-strain, the plastic region, the ground response curve, and the dilatability of surrounding rock. The results showed that the plastic radius , the residual radius , and radial displacement of surrounding rock first decreased and then increased with increasing intermediate principal stress coefficient b from 0 to 1, with the minimums occurring at b = 0.75. On the contrary, the peak and rate of variation of the dilatancy coefficient first increased and then decreased with increasing b and the dilatancy coefficient gradually transitioned from nonlinear to linear variation. Meanwhile, the inhibition of the plastic radius and radial displacement gradually weakened with increasing support pressure, whereas the dilatancy coefficient of the tunnel opening gradually increased.

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