Abstract: The determination of mechanical properties of a deformation zone is the first step in the geomechanical study.Some new concepts and methods have been proposed and can be used for quantitative characterization of mechanical properties of deformation zones.Natural deformational zones are commonly the result of general shear,a combination of pure shear(coaxial contraction or extension) and simple shear.In order to describe quantitatively their relative contributions,the kinematic vorticity number(W_k) is introduced and simply defined as cos υ,where υ is the angle between two eigenvectors containing the shear directions in the principal deformation plane(XZ-plane or ac-plane).For pure shear,υ=90° and W_k=0,and for simple shear,υ=0° and W_k=1.General shear is a combination of the above two,whose υ ranges between 0° and 90° and W_k from 0 to 1.The kinematic vorticity numbers may be signed as positive or negative.The positive and negative signs represent thinning and thickening of deformation zones respectively.The angle υ between the eigenvectors is available in several ways by means of polar-Mohr constructions.
W_k can be given by the orientation of the maximum principal stress(σ₁):W_k=sin 2ξ,where ξ is the angle between σ₁ and the normal to the deformation zone.Therefore,the related W_k and the mechanical properties of the deformation zone can be determined. Based on the maximum effective moment criterion,M_eff=0.5(σ₁-σ₃)Lsin2 αsinα,where the angle α between a ductile deformation zone and the maximum principal compressional stress axis is 55°.The relationship can be used to infer the stress-orientation and,potentially,the value of the differential stress when the deformation zone formed.