A note on vertical cuts in homogeneous soils

1993 ◽  
Vol 30 (5) ◽  
pp. 859-862 ◽  
Author(s):  
D.N. Singh ◽  
P.K. Basudhar
Keyword(s):  
Finite Element ◽  
Nonlinear Programming ◽  
Lower Bound ◽  
Limit Load ◽  
Cohesive Soils ◽  
Stability Number ◽  
Discrete Elements ◽  
Programming Technique ◽  
The Stability ◽  
Frictional Soils

In this note, the modified Lysmer method based on discrete elements and nonlinear programming technique has been extended to study the stability of a vertical cut in both homogeneous cohesive and cohesive–frictional soils to obtain lower bound solutions. For saturated clays under undrained condition, the calculated stability number (3.69) is closer to the upper bound value (3.78) than the lower bound value (3.64) reported in the literature until now. For cohesive–frictional soils, the obtained lower bound limit load compares well with that using a finite-element elastoplastic solution. Key words : lower bound, vertical cut, cohesive soils, stability number, discrete element, nonlinear programming.

The ultimate pullout capacity of anchors in frictional soils

2006 ◽  
Vol 43 (8) ◽  
pp. 852-868 ◽  
Author(s):  
R S Merifield ◽  
S W Sloan
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Limit Analysis ◽  
Numerical Study ◽  
Past Research ◽  
Pullout Capacity ◽  
Current Design ◽  
Pullout Load ◽  
Ultimate Pullout Capacity ◽  
Frictional Soils

During the last 30 years various researchers have proposed approximate techniques to estimate the uplift capacity of soil anchors. As the majority of past research has been experimentally based, much current design practice is based on empiricism. Somewhat surprisingly, very few numerical analyses have been performed to determine the ultimate pullout loads of anchors. This paper presents the results of a rigorous numerical study to estimate the ultimate pullout load for vertical and horizontal plate anchors in frictional soils. Rigorous bounds have been obtained using two numerical procedures that are based on finite element formulations of the upper and lower bound theorems of limit analysis. For comparison purposes, numerical estimates of the break-out factor have also been obtained using the more conventional displacement finite element method. Results are presented in the familiar form of break-out factors based on various soil strength profiles and geometries and are compared with existing numerical and empirical solutions.Key words: anchor, pullout capacity, finite elements, limit analysis, lower bound, sand.

Accelerated Limit Loads Using Repeated Elastic Finite Element Analyses

2003 ◽  
Author(s):  
Prasad Mangalaramanan
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Limit Load ◽  
Finite Element Analyses ◽  
Limit Loads ◽  
Bound Theorem

This paper demonstrates the limitations of repeated elastic finite element analyses (REFEA) based limit load determination that uses the classical lower bound theorem. The r-node method is prescribed as an alternative for obtaining better limit load estimates. Lower bound aspects pertaining to r-nodes are also discussed.

Seismic stability of a long unlined circular tunnel in sloping ground

2016 ◽  
Vol 53 (8) ◽  
pp. 1346-1352 ◽  
Author(s):  
Sounik Kumar Banerjee ◽  
Debarghya Chakraborty
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Plastic Zone ◽  
Slope Angle ◽  
Seismic Stability ◽  
Circular Tunnel ◽  
Infinite Slope ◽  
Sloping Ground ◽  
The Stability ◽  
Seismic Forces

The stability of an unlined long circular tunnel underneath an infinite slope is examined with the inclusion of seismic body forces. The study is carried out by using the lower bound finite element limit analysis. The values of γH/c are plotted as a function of H/D, [Formula: see text], β, and kh in the form of charts. The magnitude of γH/c is found to decrease consistently with an increase in β and kh. With an increase in the magnitude of β and kh, the plastic zone around the periphery of the tunnel becomes more and more asymmetric. The stability charts presented in this note would be useful for examining the effect of slope angle on the stability of an unsupported circular tunnel under seismic forces.

Z-Factors for Feeder Bends With Planar Axial Flaws

2009 ◽  
Author(s):  
Bogdan S. Wasiluk ◽  
Douglas A. Scarth
Keyword(s):  
Fracture Toughness ◽  
Finite Element ◽  
Lower Bound ◽  
Nuclear Reactors ◽  
Small Diameter ◽  
Limit Load ◽  
Finite Element Models ◽  
Straight Pipe ◽  
Bend Testing ◽  
Testing Program

Article C-6000 of Appendix C of ASME Section XI includes Z-factor load multipliers for straight pipes with circumferential flaws. Application of this article is limited to straight pipes with nominal pipe size (NPS) larger than 4 and materials with fracture toughness JIc higher than 105 kJ/m2. Section XI of the ASME B&PV Code does not provide Z-factors for pipes with axial flaws, even for pipes with NPS≥4. Feeders are small diameter pipes (NPS≤2.5) used in a primary heat transport system in the CANDU nuclear reactors. Developments of Z-factor load multipliers for warm-bent feeder bends with axial flaws under pressure are presented in this paper. An empirical approach was adopted using experimental results from the Feeder Bend Testing Program founded by the CANDU Owners Group. The elastic-plastic fracture mechanics stress has been defined by failure stress from the experiments. Limit load solutions for elbow/bends recently published by Kim et al. were discussed. Additionally, lower bound limit load simulations were performed using finite element models implemented for ANSYS. The results from straight pipe models exhibited good correlation with analytical solution. Numerical simulations for elbows/bends showed analogous trends for limit load of elbow/bends with axial cracks as reported by Kim et al.

Limit Load Estimation Using Plastic Flow Parameter in Repeated Elastic Finite Element Analyses

2002 ◽  
Vol 124 (4) ◽  
pp. 433-439 ◽  
Author(s):  
L. Pan ◽  
R. Seshadri
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Plastic Flow ◽  
Flow Parameter ◽  
Limit State ◽  
Limit Load ◽  
Finite Element Analyses ◽  
Finite Element Discretization ◽  
Element Discretization ◽  
Linear Elastic

The procedures described in this paper for determining a limit load is based on Mura’s extended variational formulation. Used in conjunction with linear elastic finite element analyses, the approach provides a robust method to estimate limit loads of mechanical components and structures. The secant modulus of the various elements in a finite element discretization scheme is prescribed in order to simulate the distributed effect of the plastic flow parameter, μ0. The upper and lower-bound multipliers m0 and m′ obtained using this formulation converge to near exact values. By using the notion of “leap-frogging” to limit state, an improved lower-bound multiplier, mα, can be obtained. The condition for which mα is a reasonable lower bound is discussed in this paper. The method is applied to component configurations such as cylinder, torispherical head, indeterminate beam, and a cracked specimen.

Upper and lower bound limit and shakedown loads for hollow tubes with axisymmetric internal projections under axial loading

2001 ◽  
Vol 36 (6) ◽  
pp. 595-604 ◽  
Author(s):  
S. J Hardy ◽  
A. R Gowhari-Anaraki ◽  
M. K Pipelzadeh
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Axial Loading ◽  
Limit Load ◽  
Analysis Procedure ◽  
Elastic Analysis ◽  
Elastic Plastic ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Elastic Compensation Method

In this paper, the elastic compensation method proposed by Mackenzie and Boyle is used to estimate the upper and lower bound limit (collapse) loads and the upper and lower bound shakedown loads for hollow tubes with axisymmetric internal projections subjected to axial loading. The method is based on an iterative elastic analysis procedure and the application of lower and upper bound limit load theorems. Four different geometries with a range of stress concentration factors (from low to high) are considered. Elastic-plastic finite element predictions for collapse and shakedown pressure are found to be within these upper and lower bound estimates. The method is particularly useful because it is founded on an iterative elastic approach and does not require extensive and complex elastic-plastic finite element computations.

Mesh-Free Lower Bound Limit Analysis

2015 ◽  
Vol 12 (01) ◽  
pp. 1350105 ◽  
Author(s):  
S. M. Binesh ◽  
A. Gholampour
Keyword(s):  
Lower Bound ◽  
Stress Field ◽  
Optimization Problem ◽  
Soil Mechanics ◽  
Limit Load ◽  
Computer Code ◽  
Numerical Approach ◽  
Integration Scheme ◽  
Programming Technique ◽  
Mesh Free

A novel numerical approach is developed for computing lower bound limit load in soil mechanics problems under plane strain condition. In the presented technique, there is no need to mesh in the traditional sense, and a lower bound solution is obtained. To develop the lower bound optimization problem, a statically admissible stress field is constructed by Shepard's shape functions in conjunction with the stabilized nodal integration scheme. The linearized Mohr–Coulomb criterion is adopted to satisfy the plastic admissibility of the generated stress field. The obtained optimization problem with a considerable reduced number of constraints has been solved by the linear programming technique. Based on the derived formulations, a computer code has been developed and the accuracy and efficiency of proposed method is demonstrated by solving some examples at the end of the paper.

Stability of dual square tunnels in cohesive-frictional soil subjected to surcharge loading

2014 ◽  
Vol 51 (8) ◽  
pp. 829-843 ◽  
Author(s):  
Kentaro Yamamoto ◽  
Andrei V. Lyamin ◽  
Daniel W. Wilson ◽  
Scott W. Sloan ◽  
Andrew J. Abbo
Keyword(s):  
Finite Element ◽  
Upper Bound ◽  
Limit Analysis ◽  
Ground Surface ◽  
Interface Condition ◽  
Design Stage ◽  
Tunnel Stability ◽  
Surcharge Loading ◽  
The Stability ◽  
Frictional Soils

The stability of dual square tunnels in cohesive-frictional soils subjected to surcharge loading has been investigated theoretically and numerically assuming plane strain conditions. From the viewpoint of the efficient utilization of underground space for human activities, noncircular openings and tunnels should be preferred in the design stage. Despite the importance of this issue, previous research on the subject is very limited. At present, no generally accepted design or analysis method is available to evaluate the stability of multiple tunnels–openings in cohesive-frictional soils. In the design stage, it is important to consider the interaction effects of dual tunnels. Unlike the case of a single tunnel, the centre-to-centre distance appears as a new parameter that must be considered and plays a key role in tunnel stability. In this study, continuous loading is applied to the ground surface and a smooth interface condition is modelled. For a series of tunnel size-to-depth ratios and material properties, rigorous lower- and upper-bound solutions for the ultimate surcharge loading are obtained by applying finite element limit analysis techniques. For practical suitability, the results are presented in the form of dimensionless stability charts and a table with the actual tunnel stability numbers closely bracketed from above and below. As an additional verification of the solutions, upper-bound rigid-block mechanisms have been developed, and the predicted collapse loads from these mechanisms are compared with those from finite element limit analysis. Finally, a discussion is presented regarding the location of the critical tunnel spacing between dual square tunnels where interaction no longer occurs.

Linear Stability Analysis of Space Compressive Structure of the Inverted-V Combinatorial Jib

2012 ◽  
Vol 510 ◽  
pp. 182-190
Author(s):  
Wen Jun Li ◽  
Xiao Lei Xiong ◽  
Xi Wei Dai ◽  
Qi Cai Zhou
Keyword(s):  
Finite Element ◽  
Limit Load ◽  
Shear Angle ◽  
Combinatorial Structure ◽  
Shear Load ◽  
Element Calculation ◽  
Shearing Force ◽  
Linear Buckling ◽  
The Stability ◽  
Linear Buckling Analysis

In order to study the problem of stability-losing load of the super-big crane jib with the inverted-V shape, this paper completed theoretical analysis, simulation and verification. Based on the stability-losing load formula considering shearing-force influence of compressed solid column, the limit load formula of the inverted-V combinatorial jib was obtained. Then, the method of force was applied to getting the shear angle formula of the inverted-V combinatorial jib under unit shear load. After using the proved formulas and software SAP2000 in linear buckling analysis of 28 combinatorial jibs consisting of two kinds of typical-section rods, the results demonstrated that: As for combinatorial structure consisting of cross-shaped web members, the error between results of the proved limit load formula and finite element calculation was within-5% when the aspect ratio of the inverted-V combinatorial jib was above 3.

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