Mixed boundary value problems in soil mechanics

Abstract

The stress-strain law for an ideal soil formulated in a recent paper [1]<inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="cubed"> <mml:semantics> <mml:msup> <mml:mi/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> <mml:annotation encoding="application/x-tex">^{3}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is applied here to obtain the velocity equations referred to the stress characteristic lines in plane strain problems. Simple velocity fields associated with families of straight characteristic lines are then examined, together with discontinuities in the velocity field. The results are applied to obtain the incipient velocity field for the indentation of a semi-infinite mass of material by a flat punch or footing, and to solve the problem of indentation by a lubricated wedge.