Engineering Rock Mechanics
208 Rock dynamics and time-dependent aspects Figure 13.1 Examples of visible effects of (a) high and (b) low strain rates on roc ...
Stress waves 209 an infinitesimal cube of material is accelerating, and applying Newton’s Second Law of Motion, these equations ...
2 1 0 Rock dynamics and time-dependent aspects customary engineering constants E and v for isotropic materials through A = Ev/[( ...
Stress waves 21 1 Particle motion r Particie A\\\\ II I I1 motion I propagation Direction of Direction of wave propagation (a) L ...
2 1 2 Rock dynamics and time-dependent aspects bonded to bars Steel SPeclmen Steel input rod ouput rod (a) Hopkinson bar (a) Pie ...
Time-dependency 2 1 3 c;, c; Interface at x = 0 c, = vp c2 = \'\ Incident wave Snell's law aoolie? to reflection and Incident P- ...
21 4 Rock dynamics and time-dependent aspects whilst the theory of elasticity is of assistance in understanding and analysing th ...
Time-dependency 2 1 5 Rheological models These are analogues of different material behaviour, formed from assemblages of mechani ...
2 1 6 Rock dynamics and time-dependent aspects Generalized Kelvin substance Burgers substance Elastoviscoplastic (Bingham) subst ...
Time-dependency 2 1 7 which upon differentiation gives dEs-dEE I de v. dt dt dt Differentiating the fundamental constitutive rel ...
21 8 Rock dynamics and time-dependent aspects -3 € t-4 ) o=o,e non-linear relaxation. These two types of behaviour are illustrat ...
Time-dependency 2 1 9 However, for constant strain, d&ldt=O, the basic differential equation reduces to 0 = EE, with the res ...
220 Rock dynamics and time-dependent aspects E= E+ E*, 6= a+ or: and 6= &+ 6* where the overbar represents spherical and dil ...
Time-dependency in rock engineering 22 1 Pande et al. (1990). Because time-dependency is ubiquitous in rock mechanics problems, ...
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Rock mechanics 74 interactions and rock engineering systems (RES) In this chapter, we introduce a method of structuring all the ...
224 Rock mechanics interactions and rock engineering systems (RES) Discontinuous rock mass / Local stress field affected by -/ d ...
Interaction matrices 225 these concepts or subjects. The matrix presentation is not merely a peda- gogic device: it serves to id ...
226 Rock mechanics interactions and rock engineering systems (RES] + = Figure 14.2 A 2 x 2 matrix illustrating the positioning o ...
Interaction matrices 227 that shear strain involves an interaction between the axes because the amount of shear strain in the x- ...
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