Simple graphical constructions for the direction of shear

Lisle, Richard J.

doi:10.1016/s0191-8141(98)00018-2

Cited by 25 publications

(10 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The solution of this problem is addressed by a series of the publications. Some refer ences can be found, e.g., in (Lisle, 1998). The sug gested methods mainly rely on the assumption that the full stress tensor T is given.…”

Section: The Graphical Construction Of Vector P On a Generally Orientmentioning

confidence: 99%

“…The shape of the dependence is controlled by the parameter ϑ 1 -the acute angle between the normal vectors n of the family of elementary planes and axis T 1 . It is worth noting that Lisle (1998) (see also (Ramsay and Lisle, 2000)) developed a graphical pro cedure for constructing the direction p of the shear stress vector with given n and T R . However, in contrast to the method suggested in the present paper, Lisle's technique fundamentally requires an intermediate step of constructing the projection of the shear stress vector on one of the principal elementary planes.…”

Section: The Graphical Construction Of Vector P On a Generally Orientmentioning

confidence: 99%

See 1 more Smart Citation

Refraction of the principal stress trajectories and the stress jumps on faults and contact surfaces: Part 1. Non-constrained regular trajectories

Мухамедиев

2014

Izv., Phys. Solid Earth

View full text Add to dashboard Cite

Rock masses contain ubiquitous multiscale heterogeneities, which (or whose boundaries) serve as the surfaces of discontinuity for some characteristics of the stress state, e.g., for the orientation of principal stress axes. Revealing the regularities that control these discontinuities is a key to understanding the processes taking place at the boundaries of the heterogeneities and for designing the correct procedures for reconstruct ing and theoretical modeling of tectonic stresses. In the present study, the local laws describing the refraction of the axes of extreme principal stresses T 1 (maximal tension in the deviatoric sense) and T 3 (maximal com pression) of the Cauchy stress tensor at the transition over the elementary area n of discontinuity whose ori entation is specified by the unit normal n are derived. It is assumed that on the area n of discontinuity, fric tional contact takes place. No hypotheses are made on the constitutive equations, and a priori constraints are not posed on the orientation on the stress axes. Two domains, which adjoin area n on the opposite sides and are conventionally marked + and -, are distinguished. In the case of the two dimensional (2D) stress state, any principal stress axis on passing from domain -to domain + remains in the same quadrant of the plane as the continuation of this axis in domain +. The sign and size of the refraction angle depend on the sign and amplitude of the jump of the normal stress, which is tangential to the surface of discontinuity. In the three dimensional (3D) case, the refraction of axes T 1 and T 3 should be analyzed simultaneously. For each side, + and -, the projections of the T 1 and T 3 axes on the generally oriented plane n form the shear sectors S + and S -, which are determined unambiguously and to whose angular domains the possible directions p + and p -of the shear stress vectors belong. In order for the extreme stress axes and to be statically compatible on the generally oriented plane n, it is required that sectors S + and S -had a nonempty intersection. The direction vectors p + and p -are determined uniquely if, besides axes and , also the ratios of dif ferential stresses R + and R -(0 ≤ R ± ≤ 1) are known. This is equivalent to specifying the reduced stress tensors and The necessary condition for tensors and being statically compatible on plane n is the equal ity p + = p -. In this paper, simple methods are suggested for solving the inverse problem of constructing the set of the orientations of the extreme stress axes from the known direction p of the shear stress vector on plane n and from the data on the shear sector. Based on these methods and using the necessary conditions of local equilibrium on plane n formulated above, all the possible orientations of axes are determined if the projections of axes axes on side -are given. The angle between the projections of axes , and/or , on the plane can attain 90°. Besides the general case, also the particular cases of the contact between the degenerate stress states and the special posit...

show abstract

Section: The Graphical Construction Of Vector P On a Generally Orientmentioning

confidence: 99%

Section: The Graphical Construction Of Vector P On a Generally Orientmentioning

confidence: 99%

Refraction of the principal stress trajectories and the stress jumps on faults and contact surfaces: Part 1. Non-constrained regular trajectories

Мухамедиев

2014

Izv., Phys. Solid Earth

View full text Add to dashboard Cite

show abstract

“…1), as shown on geological maps by Wilson (1940), Thompson (1972), Moore and Thompson (1980), and Easton (1992Easton ( , 2001. Nadai (1950) and Lisle (1998). Some investigators of the Composite Arc Belt (southeastern Ontario) were skeptical about the Flinton unconformity, and concluded that the boundaries between the metaconglomerate units and adjacent rock masses originated as structural discontinuities or intrusive contacts (Rivers, 1976;Connelly, 1986;Connelly et al, 1987).…”

Section: Structural Significance Of the Flinton Groupmentioning

confidence: 99%

“…5; Nadai, 1950, p. 120-124;Ramsay, 1967, p. 126-129;Lisle, 1998). The graphic derivation of shearstrain sense is simplest where the strain ellipsoid degenerates into an oblate spheroid (pure flattening) or prolate spheroid (perfectly constrictive deformation).…”

Section: Tangential Shear Strain At Stretched Lithotectonic Boundariesmentioning

confidence: 99%

“…The investigation of tangential shear strain was therefore restricted, at most localities, to finding its direction and sense. This is accomplished by using graphic techniques developed by Lisle (1998) and Schwerdtner (1998). The theoretical basis of these techniques is covered elsewhere (Lisle, 1998;Schwerdtner, 1998;Schwerdtner and Cote, 2001), and is not be repeated in the present paper.…”

Section: Tangential Shear Strain At Stretched Lithotectonic Boundariesmentioning

confidence: 99%

See 1 more Smart Citation

L-S shape fabrics in the Mazinaw domain and the issue of northwest-directed thrusting in the Composite Arc Belt, southeastern Ontario

Schwerdtner¹,

Downey²,

Alexander³

2004

Memoir 197: Proterozoic Tectonic Evolution of the Grenville Orogen in North America

View full text Add to dashboard Cite

Many vertical sections across deeper parts of collisional orogens contain gently dipping thrusts that have the geometric style of shallow-crustal, dip-slip faults. In the southwestern Grenville Province (central and southeastern Ontario), however, structural geologists have found it difficult to document northwest-directed thrusting within large, polydeformed complexes of medium-to high-grade metamorphic rocks. This applies, in particular, to the Mazinaw domain of the eastern Composite Arc Belt, where narrow north-to east-northeast-striking ("longitudinal") zones of high strain have been linked tentatively to ductile thrusting at the sole of Elzevirian (1230-1190 Ma) or Early Ottawan (1085-1015 Ma) fold nappes. During subsequent northwestsoutheast shortening, the apparent thrusts behaved as structural detachment horizons or were subhorizontally folded, together with their wallrocks.Gravity modeling and reflection-seismic profiling have shown that in the present shallow crust most tabular rock bodies and coplanar structural surfaces (including high-strain zones and ductile faults) are horizontal or dip < <45°SE. This seems incompatible with the idea that Elzevirian and Early Ottawan thrusts acquired strong curvature in the northwest-southeast vertical plane during upright buckling of fold nappes and other southeast-dipping lithotectonic units.The longitudinal high-strain zones and their ductilely deformed wallrocks are characterized by steeply inclined to vertical planar fabrics (S) such as geometric systems of strained mineral constituents, pebbles, and volcanic fragments. Linear fabrics (L) coexist with the planar fabrics at many localities, but are commonly weak or seemingly absent. The prevalence of planar fabrics is difficult to explain by shallow-crustalstyle ductile thrusting, but these fabrics may have been produced by large-scale strains associated with the formation of midcrustal stretching thrusts.For a variety of thrust-dip options, we use L < < S fabrics to derive the local sense of tangential shear strain within and adjacent to six high-strain zones. The sense of accumulated shear strain proves to be reverse for most realistic options, even if one presumes that the zones rotated during superimposed buckle folding. Mesoscopic Zfolds are common in one high-strain zone, and attest to dextral-reverse shearing and shortening of thrust walls during Mid-to Late Ottawan deformation (1015-980 Ma). *

show abstract

Fault slip inversion methods

Pascal

2022

Paleostress Inversion Techniques

View full text Add to dashboard Cite

Simple graphical constructions for the direction of shear

Cited by 25 publications

References 14 publications

Refraction of the principal stress trajectories and the stress jumps on faults and contact surfaces: Part 1. Non-constrained regular trajectories

Refraction of the principal stress trajectories and the stress jumps on faults and contact surfaces: Part 1. Non-constrained regular trajectories

L-S shape fabrics in the Mazinaw domain and the issue of northwest-directed thrusting in the Composite Arc Belt, southeastern Ontario

Fault slip inversion methods

Contact Info

Product

Resources

About