14 - 1 Photo: B. Eade ROCK MECHANICS Instructor: Claire...

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ERTH2404/14 Rock mechanics 1 ROCK MECHANICS Instructor: Claire Samson, Ph.D., P.Eng. Photo: B. Eade
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ERTH2404/14 Rock mechanics 2 Reading assignment • Please read Kehew’s book to complement the material presented in this lecture: Chap. 7 in 3 rd Edition Chap. 6 in 2 nd Edition
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ERTH2404/14 Rock mechanics 3 Lecture objectives • Compute stress for simple 1D and 2D cases • To understand the response of rock materials to applied loads • To know how material strength is measured in the laboratory • Understand how laboratory samples and rock masses are assessed to determine their suitability for engineering work
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ERTH2404/14 Rock mechanics 4 Lecture objectives • Understand the relation between rock type and engineering properties • Appreciate how a rock mass can be weakened by a variety of discontinuities
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ERTH2404/14 Rock mechanics 5 Contents • Computing stress – 1D: Vertical lithostatic pressure – 2D: Mohr’s cycle • Deformation-response to stress • Measuring rock strength • Deere-Miller classification of intact rock • Rock-mass properties
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ERTH2404/14 Rock mechanics 6 Computing stress
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ERTH2404/14 Rock mechanics 7 Stress Stress ( ! ): Force applied per unit area [N/m 2 ] – Normal stress: component of stress perpendicular to a given plane • Compressional: to shorten a body • Tensional: to pull apart a body – Shear: component of stress applied parallel to a given plane
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ERTH2404/14 Rock mechanics 8 Shear Tension Compression Normal stresses
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ERTH2404/14 Rock mechanics 9 1D Case: Vertical lithostatic stress
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ERTH2404/14 Rock mechanics 10 Unit weight Unit weight ! [N/m 3 ]: product of density and gravity acceleration ! = " g ! : density [kg/m 3 ] g : gravity acceleration [m/s 2 ] • The product of unit weight by thickness has unit of pressure
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ERTH2404/14 Rock mechanics 11 Vertical lithostatic stress " v • Stress beneath a sequence of horizontal layers is the sum of the unit weight of each layer times its thickness – Atmospheric pressure is neglected " v = # ! i * h i • Stress responsible for compaction in sedimentary basins
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ERTH2404/14 Rock mechanics 12 Example Soil Sandstone Shale Depth to layer base Thickness Density Unit weight Individual Cumulative [m] [m] [kg/m 3 ] [N/m 3 ] [N/m 2 ] [N/m 2 ] Soil 2 2 2.0 19.6 39.2 39.2 Sandstone 10 8 3.0 29.4 235.2 274.4 Shale 11 1 3.5 34.3 34.3 308.7 Vertical lithostatic stress at layer base 0 2 4 6 8 10 12 0 100 200 300 400 Cumulative stress at layer base [N/m2] Depth [m]
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ERTH2404/14 Rock mechanics 13 2D Case: Stresses on an inclined plane
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ERTH2404/14 Rock mechanics 14 Mohr’s circle • 2D element with normal stresses applied perpendicular to its surface – By convention • Compressional stress > 0 • Tensional stress < 0 – No shear stress applied – For an unconfined element " 3 = 0
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Rock mechanics 15 ! 3
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14 - 1 Photo: B. Eade ROCK MECHANICS Instructor: Claire...

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