stress analysis

stress analysis Stress analysis is the process used to estimate the distribution of forces throughout a mass of material. In the geosciences, stress analysis can be used to ascertain whether a material is approaching, or has reached, a state of limiting equilibrium (or failure); if the appropriate stress– strain relationships are known, it can also be used to calculate the resulting deformations. Calculations of this kind are vital in many areas of engineering geology.

A stress is a force divided by the area over which it acts. If, for example, a vertical cylinder of rock, with a horizontal cross-sectional area a, is subjected to a vertical compressive force N, which will tend to reduce its height, the cylinder is then under a compressive normal stress (that is, a compressive stress acting parallel to its axis) of N/a (Fig. 1). The converse is the application of a tensile normal stress—one that tends to pull the ends of the cylinder apart—which will obviously tend to lengthen the cylinder. The customary units for stresses are newtons per square millimetre (N mm⁻²) and kilonewtons per square metre (kN m⁻²). Two stresses will usually act on any chosen plane in a mass of material. One of these is the normal stress, as described above, which acts at right-angles to the plane; the other is the shear stress, which acts along the plane, tending to distort the material as shown in Fig. 2. (It should be mentioned that in many textbooks on stress analysis tensile normal stresses are treated as positive, and compressive normal stresses are treated as negative. The opposite convention is, however, usually adopted for geomaterials (rocks and soils), because the tensile strengths of these materials tend to be low in comparison to their compressive strengths.)

Many problems in stress analysis can be analysed in two dimensions. Two normal stresses and one shear stress then need to be specified to define the state of stress at any specified point in the material (Fig. 3). More generally, stress states exist in three dimensions. Three normal stresses and three shear stresses will then need to be considered, as shown in Fig. 3a.

At any point in a continuous mass of material the stresses will change as the direction of the plane that is being considered is varied. These changes can conveniently be shown in graphical form by a Mohr's circle of stress. In practice, numerical methods, such as finite elements, are commonly used to carry out stress analysis.

In soils, which consist of uncemented, or weakly cemented, particles, there are voids between the particles. These are generally interconnected and are filled with liquid, usually water, or gas, such as air. Any stress applied to the soil may be taken, wholly or in part, by the pore fluid phase. Assuming that the fluid has no shear strength, the contribution of the fluid phase will then be to help support the normal stress. Any total normal stress will therefore be taken by a normal stress carried by the assemblage of soil particles, the effective normal stress, and the normal stress in the pore fluid. The total normal stress will therefore be the sum of the effective normal stress and the normal stress in the pore fluid. This is known as the principle of effective stress. If the soil is fully saturated, that is, if the pore space is completely filled with water, the normal stress in the pore fluid is simply the pore water pressure. If the voids are partially filled with water, the expression can be amended. If the soil has an appreciable air content, then the total normal stress is often taken as zero. Soils can thus be analysed in terms of total or effective stress. The total stress is often used for convenience, although as the shear resistance of soil derives from the interaction of the particles, the effective stress should be used.

T. Cousens