Consider the axisymmetric half-space problem shown in Fig. 14.19 for the case where only Poisson’s ratio is allowed to vary with depth coordinate v = v(z). Using cylindrical coordinates (r, θ, z) to formulate the problem, first show that the stress field can be expressed by:

Fig 14.19

Transcribed Image Text:

r = - 2 0 = duz = 24 (201 + 2 (2)1) v* v) z dur r trz= Ur %0 % = 2 (r +v (2) v) +v* (z) v aur (D -) + ur duz + z r dur Ur duz where = + + is the dilatation and v*(z) r r z equilibrium equations reduce to a r v(z) [12v(z)]] ((1+2v*)v) = 0 a Vu+((1+2*)v) = 0 dz Next show that the