By Arul M. Britto, Michael J. Gunn
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Additional resources for Critical state soil mechanics via finite elements
The matrix is gradually being converted into 'upper triangular' form. Now the process of forward elimination is started: (a) ~~ -20 -10 - 20(7/80) -10(3/40) = O. d 2 = 1/20. Solve for d l from the first equation: 10 6 d l -20d2 = WI' d, = 0 (very nearly). From the nodal displacements it is now possible to calculate the spring elongations and tensions. 3 A computer program for the displacement method Listed below is a FORTRAN program which can be used to analyse collections of springs similar to the one considered above.
2 Critical state soil mechanics gives a good qualitative account of how deformation proceeds in both 'wet' and 'dry' clays. Suppose that one particular zone in a 'wet' clay has strained more than neighbouring zones. This zone will have strain-hardened more than the surrounding soil and will thus be stronger. Further deformation takes place around this hardened zone and there is a tendency for the soil to deform in a uniform, homogeneous fashion. On the other hand, if a zone in 'dry' soil has deformed more than the surrounding soil, it will be weaker than the surrounding material.
L) three times and solving the resulting equations. In fact one can write down the quadratic straight away as f(x) ~1 1' ~! I' ,d "1 ~\I~ I~. ). I~ I !! 1 /=/1 (X3 -X)(X2 -x) (X3 (X2 - X) (X I + /3 )! 2) -X3) It is possible to see by substituting X = XI etc. that this must be the corr equation of the quadratic . An expression in this form is known as a Langragian interpolation polynomial, and the idea can clearly be extended to any number of points. Expressions of this form arise quite often in finite element theory where the nota tion 6 4 is often adopted and each of the Ni is referred to as a 'shape function '.
Critical state soil mechanics via finite elements by Arul M. Britto, Michael J. Gunn