Caption: Figure 12: Nephograms of equivalent plastic zone
at ZK275+290 section considering seepage and no seepage (KPa).
 proposed that reducing rock permeability would change pore water pressure and prompt an expansion of the plastic zone
of the rock mass that surrounded tunnels.
As a fracture mechanics parameter for small-scale yielding condition, the AK can be used for plane-strain FCG if the plastic zone
at the crack tip is small compared to crack length (a), thickness (B), and uncracked ligament (W-a).
Mechanically inhomogeneous two-layer pipe may be divided into two pipes with different mechanical properties: internal pipe 1 with modulus of elasticity [E.sub.1], Poisson's ratio [v.sub.1], limit of elasticity [[sigma].sub.e1], power index of material hardening in elastic plastic zone
[m.sub.01] and external pipe 2 with [E.sub.2], [v.sub.2], [[sigma].sub.e2] and [m.sub.02] (Fig.
Afterwards, the forward and reverse plastic zone
interaction is considered to be an essential characteristic of load sequence effects [7, 8].
The previous research [33, 34] shows a close relation between the range and shape of the plastic zone
and the stability of the roadway.
For example, Pan and Brown  proposed an approach in which the axial in situ stress of the plastic zone
is deformation-dependent and the formula for the calculation of intermediate principal stress was derived, only numerical solution through finite element method was presented.
where [V.sub.p] is the plastic zone
. When [R.sub.0] is greater than 1, the potential energy for outburst initiation is sufficient and indicates the danger of an outburst.
The micrographs indicate no plastic zone
for the neat resin (Fig.
Based on Equation (4) and nonassociated flow rules, the constitutive equation in rupture and plastic zone
is expressed as
The stress expression of the plastic zone
can be obtained by (1) and (5), shown as
According to the research of Carranza-Torres , Sharan [7, 8] presented a new solution and calculation method of critical plastic zone
using Newton-Raphson method.