scholarly journals Lower Bound Solution of Foundation Bearing Capacity beneath Strip Footing Based on Parabolic Mohr Failure Criterion

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Fang Wei ◽  
Shi Li-jun
Keyword(s):  
Lower Bound ◽  
Stress Field ◽  
Bearing Capacity ◽  
Yield Criterion ◽  
Rock Foundation ◽  
Allowable Stress ◽  
Bound Solution ◽  
Loading Tests ◽  
Lower Bound Solution ◽  
Two Parameter

The static allowable stress field of foundation under strip foundation is constructed by means of stress columns, and the calculation method of the lower bound foundation bearing capacity based on the two-parameter parabolic Mohr yield criterion is proposed. Moreover, the influence of the amount of stress columns and material mechanical parameters on the lower bound bearing capacity is analyzed. The results show that a better solution can be obtained by optimizing the static allowable stress field. However, the improvement of lower bound solution might be inefficient if the stress column amount is large enough. The stresses of the superimposition area show a reduction with the improvement of stress field; on the other hand, the superposed stresses are enhanced ever faster as the involved stress column increases. The tensile-compressive strength ratio has a moderate effect on the lower bound solution. Finally, the reliability of the proposed method is verified by some rock foundation loading tests.

scholarly journals Lower-Bound Solution of Foundation-Bearing Capacity under Circular Uniformly Distributed Load

2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Fang Wei ◽  
Wang Jiao ◽  
Zhang Wan-dongxing ◽  
Shi Li-jun
Keyword(s):  
Lower Bound ◽  
Bearing Capacity ◽  
Three Dimensional ◽  
Friction Angle ◽  
Bound Solution ◽  
Distributed Load ◽  
Uniformly Distributed Load ◽  
Soil Shear Strength ◽  
First Time ◽  
Lower Bound Solution

The semispatial static allowable stress field was constructed by three-dimensional stress columns, and the analytical lower-bound solution of bearing capacity of Mohr–Coulomb foundation beneath circular uniformly distributed load was put forward for the first time. The influence of the amount of stress columns and soil shear strength parameters on the lower-bound solution of the foundation-bearing capacity is analyzed. The research showed that (1) when the number of stress columns is more than 9 (n > 4) and the friction angle is less than 30°, the relative error between the lower-bound solution of the bearing capacity and exact solution is less than 6.6%, (2) the suggested analytical solution is applicable for common clayey materials; thus, the application scope of the analytical lower-bound solution is further expanded, and (3) the influence of cohesion on bearing capacity is linear. However, with the increase of the friction angle, the bearing capacity increases faster and faster under all cohesion levels. The correctness and effectiveness of the proposed method were verified by literature comparison.

Influence of a nonlinear failure criterion on the bearing capacity of a strip footing resting on rock mass using a lower bound approach

2003 ◽  
Vol 40 (3) ◽  
pp. 702-707 ◽  
Author(s):  
Xiaoli Yang ◽  
Jian-Hua Yin ◽  
Liang Li
Keyword(s):  
Rock Mass ◽  
Lower Bound ◽  
Stress Field ◽  
Bearing Capacity ◽  
Failure Criterion ◽  
Material Parameter ◽  
Strip Footing ◽  
Nonlinear Material ◽  
Stress Fields ◽  
Nonlinear Failure Criterion

The strength envelope of almost all geomaterials is nonlinear when one considers a wide range of stresses. Therefore, a nonlinear failure criterion needs to be used in stability analysis whenever the effects of nonlinearity are too significant to be neglected. This paper presents a lower bound solution to the bearing capacity calculation of a strip footing resting on a homogenous weightless rock mass using the nonlinear Hoek–Brown (HB) failure criterion. Two types of admissible stress fields are used to develop solutions. The first stress field has three stress legs. The second stress field has a spiral-like shape with n stress legs, where n may vary from 9 to 18 000 (even to infinity). Using two admissible stress fields, equations are derived and used for the calculation of lower bound bearing capacity values of a strip footing on rock mass. The influences of the admissible stress leg number n and the material parameter s in the nonlinear HB failure criterion are investigated. It is found that the lower bound bearing capacity calculated using the spiral-like shape admissible stress field approaches to the true optimum value as the stress leg number n increases, and the nonlinear material parameter s has a strong influence on the bearing capacity of the footing.Key words: HB failure criterion, bearing capacity, stress leg, lower bound theorem, rock.

scholarly journals Metal drawing goodness degree to which the Hollomon equation applies

2014 ◽  
Vol 20 (1) ◽  
pp. 61-71 ◽  
Author(s):  
Živko Jokovic ◽  
Nina Djapic
Keyword(s):  
Lower Bound ◽  
Tungsten Carbide ◽  
Wire Drawing ◽  
Control Group ◽  
Practical Application ◽  
Theoretical Methods ◽  
Bound Solution ◽  
Cold Wire ◽  
Lower Bound Solution ◽  
Hollomon Equation

In order to establish the cold wire drawing production, the CuNi2Si alloy passes schedule were examined by the Duckfield and Ermanok methods in two wire drawing versions: with the diamond die with an angle of 9o and the tungsten carbide die with an angle of 7o . Experiments confirmed that the CuNi2Si alloy can be successfully transformed to the wire with the diameter of 0.2 mm with properties enabling its practical application. The experimental results and the control group showed that the theoretical methods of the upper and lower bound solution can determine the values of the relevant cold wire drawing factors for the CuNi2Si alloy to which Hollomon curve applies. 

Lower Bounds to the Collapse Load of a Thick Circular Cylinder Subjected to Internal Pressure and Shear

1977 ◽  
Vol 44 (4) ◽  
pp. 766-768
Author(s):  
N. Inoue ◽  
H. Nakagawa ◽  
T. Nakayama ◽  
M. Shimono ◽  
T. Tanaka
Keyword(s):  
Lower Bound ◽  
General Solution ◽  
Circular Cylinder ◽  
Internal Pressure ◽  
Plane Strain ◽  
Lower Bounds ◽  
Mathematical Theory ◽  
Collapse Load ◽  
Bound Solution ◽  
Lower Bound Solution

A new method for obtaining statically admissible states of stress in plane strain in the mathematical theory of plasticity is presented. After deriving a general solution, the proposed procedure is exemplified by a known solution of a thick circular cylinder subjected to internal pressure. The method is applied to a thick circular cylinder subjected to internal pressure and shear, and a lower-bound solution is given.

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