scholarly journals Shear strength of clayey soils from the vicinity of Gorlice and Ciężkowice

2015 ◽  
Vol 47 (3) ◽  
pp. 225-236
Author(s):  
Tymoteusz Zydroń ◽  
Ewa Prawica
Keyword(s):  
Shear Strength ◽  
Residual Strength ◽  
Linear Equations ◽  
Clayey Soils ◽  
Angle Of Internal Friction ◽  
Strength Tests ◽  
Non Linear ◽  
Shearing Strain ◽  
Direct Shear Apparatus ◽  
Non Linear Equations

Abstract The work presents results of maximum and residual strength tests of six clayey soils from the landslide areas near Gorlice and Ciężkowice. The tests were carried out in a direct shear apparatus on samples of dimensions 60 × 60 mm that were sheared at least three times. A shearing strain rate was equal 0.1 mm·min–1, and the range of horizontal deformation of the samples was equal 20%. The results of the tests revealed that multiple shearing of the soil caused a significant decrease of its shear strength, resulting in significant changes in cohesion, and the smaller changes in the angle of internal friction. It was shown that the three-time shearing reduced the initial shear strength of about 50%, and further three series of shearing decreased it approximately 15% more. The study also showed that by using a Coulomb-Mohr shear strength linear equation, the analyzed soils had a little residual cohesion. Therefore, to describe the characteristics of the residual strength, there were used two non-linear equations proposed by Mesri and Shanien (2003) and Lade (2010), which led to the same results. It was also shown that the use of non-linear characteristics of the residual strength at low values of the normal stresses gave more unfavourable results of stability calculations in relation to the method based on the linear strength characteristic taking into consideration the presence of the residual cohesion.

scholarly journals Influence of moisture content of cohesive soils on their shear strength

2017 ◽  
Vol 2017 (5) ◽  
pp. 10-19 ◽  
Author(s):  
Tymoteusz Zydroń ◽  
Małgorzata Wojciechowska-Dymańska ◽  
Andrzej Gruchot ◽  
Tomasz Zalewski
Keyword(s):  
Shear Strength ◽  
Moisture Content ◽  
Optimum Moisture Content ◽  
Cohesive Soils ◽  
Test Results ◽  
Angle Of Internal Friction ◽  
Shearing Rate ◽  
Strength Tests ◽  
Shear Box ◽  
Direct Shear Apparatus

Influence of moisture content of two cohesive soils on their shear strength was the purpose of the tests. The shear strength tests were carried out in a standard direct shear apparatus of dimensions of the box 6 x 6 x 1,8 cm. Each sample of assumed moisture content was preliminary compacted at Proctor apparatus, then was cut using a square cutter and to set into the shear box. Each series of samples were tested at four values of moisture content: equal, lower and higher than optimum moisture content. One series of samples, sheared at moisture content higher than optimum moisture content, the shearbox during consolidation and shearing was filled with the water to the level corresponding to shearing plane. Main tests were done using shearing rate equal to 1,0 mm.min-1 and time of consolidation was equal to 12 hours. Additional tests were done using shearing rate equal to 0,05 mm.min-1 and the samples during consolidation and shearing were saturated. Test results revealed that the most beneficial values of shear strength were obtained at optimum moisture content or lower that optimum moisture content. It stated that the increase of moisture content cause decrease of angle of internal friction and the highest values of cohesion was obtained at optimum moisture content. Comparison of test results obtained for series of samples sheared at optimum moisture content revealed that saturation of soil sample and low shearing rate cause very significant reduction of obtained values of cohesion.

scholarly journals A master exceptional field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Guillaume Bossard ◽  
Axel Kleinschmidt ◽  
Ergin Sezgin
Keyword(s):  
Field Theory ◽  
Gauge Invariance ◽  
Sigma Model ◽  
Linear Equations ◽  
Field Theories ◽  
Gauge Invariant ◽  
Non Linear ◽  
Non Linear Equations

Abstract We construct a pseudo-Lagrangian that is invariant under rigid E11 and transforms as a density under E11 generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on E11 exceptional field theory and the inclusion of constrained fields that transform in an indecomposable E11-representation together with the E11 coset fields. We show that, in combination with gauge-invariant and E11-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condi- tion. For another choice, we reobtain the E8 exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the E10 sigma model.

An elliptic boundary value problem for strongly non-linear equations in unbounded domains

1977 ◽  
Vol 77 (3-4) ◽  
pp. 217-230 ◽  
Author(s):  
Vesa Mustonen
Keyword(s):  
Boundary Value Problem ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Linear Equations ◽  
Unbounded Domains ◽  
Elliptic Boundary Value Problem ◽  
Elliptic Boundary Value ◽  
Non Linear ◽  
Linear Elliptic Boundary ◽  
Non Linear Equations

SynopsisThe existence of a variational solution is shown for the strongly non-linear elliptic boundary value problem in unbounded domains. The proof is a generalisation to Orlicz-Sobolev space setting of the idea introduced in [15] for the equations involving polynomial non-linearities only.

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