Micromechanical basis for shear strength of rock discontinuities

The theoretical basis for evaluating shear strength in rock joints is presented and used to derive an equation that governs the relationship between tangential and normal stress on the joint during situations of slippage between the joint faces. The dependent variables include geometric dilatancy, the instantaneous friction angle, and a parameter that considers joint surface roughness. The effect roughness is studied, and the aforementioned formula is used to analyse joints under different conditions. A mathematical expression is deduced that explains Barton's value for the joint roughness coefficient (JRC) according to the roughness geometry. In particular, when the Hoek and Brown failure criterion is used for a rock in the contact with the surface roughness plane, it is possible to determine the shear strength of the joint as a function of the relationship between the uniaxial compressive strength of the wall with the normal stress acting on the wall. Finally, theoretical results obtained for the geometry of a three-dimensional joint are compared with those of the Barton's formulation

Ultimate bearing capacity at the tip of a pile in rock based on the modifed Hoek-Brown criterion

Highlights of this paper: a method for calculating the ultimate bearing capacity at the tip of a pile is presented; ultimate bearing capacity is generalized for the modified Hoek–Brown criterion; perfect plasticity, isotropy, weightless rock media, without inertial forces, Meyerhof׳s hypothesis are considered; all the formulation can be programmed in a spreadsheet.

Mathematical development of stress-strain law for rock block contacts

The fracture behavior of rock block contacts has been studied for many years. Unfortunately, up to now, there is not a rigorous formulation or a solid theoretical foundation to support it. A mathematical development to represent the failure mechanism which occurs in the contacts between rock blocks is presented to evaluate the performance of breaking mechanism of such blocks relating it to the morphology of the contact and mechanical parameters of the material. The examined framework includes the evaluation of the surface roughness of first order in the failure mechanism of the granular particles of large size and the development of a theoretical model describing the morphology of the contact between rock blocks.

Characterization of rock joints by fractal analysis

From a physical perspective, a joint experiences fracturing processes that affect the rock at both microscopic and macroscopic levels. The result is a behaviour that follows a fractal structure. In the first place, for saw-tooth roughness profiles, the use of the triadic Koch curve appears to be adequate and by means of known correlations the JRC parameter is obtained from the angle measured on the basis of the height and length of the roughnesses. Therefore, JRC remains related to the geometric pattern that defines roughness by fractal analysis. In the second place, to characterise the geometry of irregularities with softened profiles, consequently, is proposed a characterisation of the fractal dimension of the joints with a circumference arc generator that is dependent on an average contact angle with regard to the mid-plane. The correlation between the JRC and the fractal dimension of the model is established with a defined statistical ratio.

The dialogues of Plato,

v. 1. Charmides. Lysis. Laches. Protagoras. Euthydemus. Cratylus. Phaedrus. Ion. Symposium.--v. 2. Meno. Euthyphro, Apology, Crito, Phaedo, Gorgias, Appendix I: Lesser Hippias, Alcibiades I. Menexenus. Appendix II: Alcibiades II. Eryxias.--v. 3. Republic. Timaeus. Critias.--v. 4. Parmenides. Theaetetus. Sophist. Statesman. Philebus.--v. 5. Laws. Index to the writings of Plato.

The works of Plato. A new and literal version chiefly from the text of Stallbaum ...

Vol. I translated by Henry Cary, vol. II, by Henry Davis, vols. III-VI, by George Burges.

The works of Plato /

v. 1. The Apology of Socrates, Crito, Phaedo, Gorgias, Protagoras, Phaedrus, Theaetetus, Euthyphron, and Lysis -- v. 2. The Republic, Timaeus, and Critias -- v. 3. Meno, Euthydemus, The sophist, The statesman, Cratylus, Parmenides, and the Banquet -- v. 4. Philebus, Charmides, Laches, Menexenus, Hippias major, Hippias minor, Ion, First Alcibiades, Second Alcibiades, Theages, The rivals, Hipparchus. Minos, Clitopho, The epistles -- v. 5. The laws -- v. 6. The doubtful works ... with lives by Plato by Diogenes Laertius, Hesychius, and Olympiodorus; introductions to his doctrines, by Alcinous and Albinus; the notes of Thomas Gray, and a general index.

Alcibiade, jeune homme : orné de planches en taille douce : seconde partie

Mode of access: Internet.

Alcibiade, enfant... : premiere partie

Mode of access: Internet.

The divine and moral works of Plato,

The first Alcibiades.- The second Alcibiades.- Theages.- Eutyphron.- Crito.- Phedon.- Laches.- The rivals.- Protagoras.- Socrates's apology.

Six of Plutarch's Greek lives.

Filing title: Vitae parallelae. English. Selection.

Platonis Opera quae feruntur omnia : ad codices denuo collatos /

Text in Greek; introd. and notes in Latin.

The works of John Otway, consisting of his plays, poems, and letters. With a sketch of his life, enlarged from that written by Dr. Johnson.

I. Alcibiades. Don Carlos, prince of Spain. Titus and Berenice. The cheats of Scapin. Friendship in fashion. The soldier's fortune.--II. The atheist; or, The second part of The soldier's fortune. The orphan. The history and fall of Caius Marius. Venice preserved. Poems and letters.

Platon's werke einzeln erklärt und in ihrem zusammenhange dargestellt,

Vol. 2-3, Erfurt, C. Villaret.

The works of Mr. Thomas Otway : containing his plays, poems, and love-letters.

v. 1. Alcibiades. Don Carlos. Titus and Berenice. Friendship in fashion. The soldiers fortune.--v. 2. The atheist. The orphan. Caius Marius. Venice preserved.