Royal Melbourne Institute of Technology
CIVE 1105
Why study stress in rock mechanics? Three basic reasons for an engineer to understand stress in the context of rock mechanics: 1) Pre-existing stress state in the ground; 2) Engineering activities change the stress fields in rock masses – change of stress leads to instability; almost all failure criteria are expressed as a f
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Why study stress in rock mechanics? Three basic reasons for an engineer to understand stress in the context of rock mechanics: 1) Pre-existing stress state in the ground; 2) Engineering activities change the stress fields in rock masses – change of stress leads to instability; almost all failure criteria are expressed as a function of stress quantities. 3) Stress is complex: it is a tensor (Note the difference between a scalar, a vector and a tensor). It is difficult to comprehend without a clear understanding of the fundamentals. A scalar is a quantity with magnitude only, e.g. temperature, time; A vector is a quantity with magnitude and direction, e.g. force, velocity and acceleration; A tensor is a quantity with magnitude, direction and ‘plane under consideration’. e.g. stress and moment of inertia. Stress components (a) Normal forces and shear forces. (b) Normal stresses and shear stresses. The normal and shear stress components are the normal and shear forces per unit area. A solid can sustain shear forces, whereas a liquid or gas cannot. A liquid or gas contains a pressure, which acts equally in all directions. Definition of stress A F σ = Resolution of a normal force. A force F can always be resolved to two components: normal component Fn is found in a direction θ from F = Fcosθ; and shear component Fs = Fsinθ Stress within rock The normal stress and shear stress can be defined as: Normal stress: Shear stress: The forces that are required to act in order to maintain equilibrium on a small area of a surface created by cutting through the rock. On a very small area ∆A, equilibrium can be maintained by the normal force ∆N and the shear force ∆S. The stress components on a small cube within the rock The principal stresses The state of stress at a point is defined by the six independent The principal stresses are defined as those components: normal components of stress that act on planes that have shear stress components with zero magnitude. It is convenient to specify the stress state using these principal stresses because they provide direct information on the maximum and minimum values of the normal stress components. We make the convention that
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