scholarly journals Analysis of Inclined Strip Anchors in Sand Based on the Block Set Mechanism

2014 ◽  
Vol 553 ◽  
pp. 422-427 ◽  
Author(s):  
S.B. Yu ◽  
J.P. Hambleton ◽  
Scott William Sloan
Keyword(s):  
Upper Bound ◽  
Limit Analysis ◽  
Experimental Studies ◽  
Collapse Mechanism ◽  
Uplift Capacity ◽  
Collapse Mechanisms ◽  
Kinematic Method ◽  
The Subject ◽  
Uplift Resistance ◽  
Modelling Assumptions

Anchors are widely used in foundation systems for structures requiring uplift resistance. As demonstrated by numerous theoretical and experimental studies on the subject, uncertainty remains as to both the theoretical uplift capacity of anchors in idealised soils and the suitability of the various modelling assumptions in capturing the responses observed during tests. This study, which deals exclusively with the theoretical uplift capacity, presents newly obtained predictions of uplift capacities and the corresponding collapse mechanisms for inclined strip anchors in sand. The analysis is based on the upper bound (kinematic) method of limit analysis and the so-called block set mechanism, in which a collapse mechanism consisting of sliding rigid blocks is optimised with respect to interior angles and edges of the blocks. It is demonstrated that the method provides lower (better) estimates of uplift capacity in some cases compared to previous upper bound calculations. Also, variations in the predicted collapse mechanism with changes in embedment and inclination are assessed in detail.

Mechanical Calculation for Collapse Mechanism of Surrounding Rock on Shallow Tunnel

2014 ◽  
Vol 580-583 ◽  
pp. 1148-1152
Author(s):  
Ying Peng ◽  
Jun Sheng Yang ◽  
Yan Hua Shen ◽  
Jian Hua Liu
Keyword(s):  
Upper Bound ◽  
Limit Analysis ◽  
Earth Pressure ◽  
Surrounding Rock ◽  
Collapse Mechanism ◽  
Shallow Tunnel ◽  
Upper Bound Method ◽  
Collapse Mechanisms ◽  
Surrounding Rock Pressure

The upper bound method of limit analysis is used for surrounding pressure calculation of shallow tunnel. Two rigid-block translational collapse mechanisms are assumed for shallow tunnel and the corresponding formulas are deduced. The earth pressure of shallow tunnel has been transformed into a mathematic optimization problem, we can get optimization solutions for the surrounding rock pressure by corresponding calculating program. It is concluded that the upper bound method of limit analysis is a feasible approach for the determination of surrounding pressures on shallow tunnel.

On Dynamic Cycle Collapse of Circular Plates

1999 ◽  
Vol 66 (1) ◽  
pp. 250-253 ◽  
Author(s):  
P. D. Chinh
Keyword(s):  
Circular Plate ◽  
Upper Bound ◽  
Point Load ◽  
Circular Plates ◽  
Load Effect ◽  
Collapse Mechanisms ◽  
Kinematic Method ◽  
Dynamic Cycle ◽  
Incremental Collapse

The upper bound kinematic method, which is based on a reduced kinematic formulation and involves construction of fictitious elastic moment fields and potential incremental collapse mechanisms, is used to evaluate the dynamic cycle collapse loads for a symmetrically loaded circular plate. The respective nonshakedown curves are constructed, A point load effect is discussed.

A Simplified Kinematic Method for 3D Limit Analysis

2016 ◽  
Vol 846 ◽  
pp. 342-347 ◽  
Author(s):  
J.P. Hambleton ◽  
Scott William Sloan
Keyword(s):  
Upper Bound ◽  
Limit Analysis ◽  
Three Dimensional ◽  
Yield Condition ◽  
Limit Load ◽  
Computational Techniques ◽  
Simple Formulation ◽  
Planar Velocity ◽  
Collapse Mechanisms ◽  
Second Order Cone

The kinematic (upper bound) method of limit analysis is a powerful technique for evaluating rigorous bounds on limit loads that are often very close to the true limit load. While generalized computational techniques for two-dimensional (e.g., plane strain) problems are well established, methods applicable to three-dimensional problems are relatively underdeveloped and underutilized, due in large part to the cumbersome nature of the calculations for analytical solutions and the large computation times required for numerical approaches. This paper proposes a simple formulation for three-dimensional limit analysis that considers material obeying the Mohr-Coulomb yield condition and collapse mechanisms consisting of sliding rigid blocks separated by planar velocity discontinuities. A key advantage of the approach is its reliance on a minimal number of unknowns, can dramatically reduce processing time. The paper focuses specifically on tetrahedral blocks, although extension to alternative geometries is straightforward. For an arbitrary but fixed arrangement of blocks, the procedure for computing the unknown block velocities that yield the least upper bound is expressed as a second-order cone programming problem that can be easily solved using widely available optimization codes. The paper concludes with a simple example and remarks regarding extensions of the work.

scholarly journals Application of discontinuity layout optimization to three-dimensional plasticity problems

2013 ◽  
Vol 469 (2155) ◽  
pp. 20130009 ◽  
Author(s):  
Samuel Hawksbee ◽  
Colin Smith ◽  
Matthew Gilbert
Keyword(s):  
Upper Bound ◽  
Limit Analysis ◽  
Three Dimensional ◽  
Layout Optimization ◽  
Benchmark Problems ◽  
Cone Programming ◽  
Yield Criteria ◽  
Collapse Mechanisms ◽  
Second Order Cone ◽  
Programming Techniques

A new three-dimensional limit analysis formulation that uses the recently developed discontinuity layout optimization (DLO) procedure is described. With DLO, limit analysis problems are formulated purely in terms of discontinuities, which take the form of polygons when three-dimensional problems are involved. Efficient second-order cone programming techniques can be used to obtain solutions for problems involving Tresca and Mohr–Coulomb yield criteria. This allows traditional ‘upper bound’ translational collapse mechanisms to be identified automatically. A number of simple benchmark problems are considered, demonstrating that good results can be obtained even when coarse numerical discretizations are employed.

Seismic horizontal pullout capacity of vertical anchors in sands

2002 ◽  
Vol 39 (4) ◽  
pp. 982-991 ◽  
Author(s):  
Jyant Kumar
Keyword(s):  
Upper Bound ◽  
Limit Analysis ◽  
Logarithmic Spiral ◽  
Friction Angle ◽  
Wall Friction ◽  
Pullout Capacity ◽  
Pullout Resistance ◽  
Collapse Mechanisms ◽  
Upper Bound Limit Analysis ◽  
Soil Interface

The problem of finding the horizontal pullout capacity of vertical anchors embedded in sands with the inclusion of pseudostatic horizontal earthquake body forces, was tackled in this note. The analysis was carried out using an upper bound limit analysis, with the consideration of two different collapse mechanisms: bilinear and composite logarithmic spiral rupture surfaces. The results are presented in nondimensional form to find the pullout resistance with changes in earthquake acceleration for different combinations of embedment ratio of the anchor (λ), friction angle of the soil (φ;), and the anchor-soil interface wall friction angle (δ). The pullout resistance decreases quite substantially with increases in the magnitude of the earthquake acceleration. For values of δ up to about 0.25–0.5φ, the bilinear and composite logarithmic spiral rupture surfaces gave almost identical answers, whereas for higher values of δ, the choice of the logarithmic spiral provides significantly smaller pullout resistance. The results compare favorably with the existing theoretical data.Key words: anchors, earthquakes, failure, limit analysis, sands.

scholarly journals Limit Analysis of Collapse Mechanisms for Tunnel Roofs Subjected to Pore Water Pressure: A Numerical Approach

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Jing-jing Liu ◽  
Tie-lin Chen ◽  
Chang-ling Xie ◽  
Jian-hua Tian ◽  
Yu-xin Wei
Keyword(s):  
Pore Water ◽  
Limit Analysis ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Numerical Approach ◽  
Collapse Mechanism ◽  
Upper Bound Theorem ◽  
Collapse Mechanisms ◽  
Support Force ◽  
Function Expression

The collapse mechanism of a circular unlined tunnel roof subjected to the pore water pressure under plane strain conditions is investigated in this article. First, the model of calculating the function expression of the detaching surface for the collapsing block is formed in the framework of the upper bound theorem of limit analysis and the extremum principle. The analytical solution of the pore water pressure around the tunnel in a two-dimensional steady seepage field is employed in the equations of the model. Then, the numerical approach based on the Runge–Kutta algorithm and traversal search method is proposed to solve the complex equations. The obtained expression of the detaching surface for the collapsing block provides the shape of the collapsing block and a theoretical basis for designing the support force for tunnels. The proposed limit analysis method and numerical approach are verified by comparing with existing theoretical solutions and the numerical simulation result, and they are suitable for deep, shallow tunnels and layered strata. Moreover, the effects of different parameters on the collapse mechanism are investigated, and qualitative results are provided.

Vertical uplift capacity of horizontal anchors using upper bound limit analysis and finite elements

2008 ◽  
Vol 45 (5) ◽  
pp. 698-704 ◽  
Author(s):  
Jyant Kumar ◽  
K. M. Kouzer
Keyword(s):  
Finite Elements ◽  
Upper Bound ◽  
Limit Analysis ◽  
Friction Angle ◽  
Soil Mass ◽  
Flow Rule ◽  
Uplift Capacity ◽  
Collapse Load ◽  
Upper Bound Limit Analysis ◽  
Associated Flow Rule

The vertical uplift capacity of strip anchors embedded horizontally at shallow depths in sand is examined by using an upper bound limit analysis in conjunction with finite elements and linear programming. Velocity discontinuities were allowed along the interfaces of all the elements. The plastic strains within elements were incorporated by using an associated flow rule. The collapse load was expressed in terms of a nondimensional uplift factor Fγ, which was found to increase continuously with an increase in both embedment ratio (λ) and the friction angle (ϕ) of sand. Even though the analysis considers the development of plastic strain within all elements, however, at collapse, the soil mass just above the anchor was found to move as a single rigid block bounded by planar rupture surfaces making an angle ϕ with the vertical. The results were found to be almost the same as reported in the literature for those based upon a simple rigid wedge mechanism.

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