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Shear strength represents the resistance of a soil to failure in shear, a concept required in analysis for the stability of soil masses. If at a point on any plane within a soil mass the shear stress becomes equal to the shear strength of the soil, then failure will occur at that point, where material behavior changes from linearly elastic to perfectly plastic. Since shear stress in a soil can be resisted only by the skeleton of solid particles, shear strength (where the material yields: t τf) should be expressed as a function of effective normal stress at failure (σf’), where c’ is the effective cohesion intercept (stress-dependent component) and q’ is Φ' is the effective angle of shearing resistance or the internal angle of friction (stress-independent component), respectively:
tf = c¢ + s¢f tanf¢τf = c' + σ'ftanΦ'.
Failure will therefore occur at any point in the soil where a critical combination of shear stress and effective normal stress develops.
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- The envelope is represented by the straight line defined by equation 1, from which the parameters c’and Φ’ are found. These are referred to as the tangent parameters and are only valid over a limited stress range. If the failure envelope is slightly curved the parameters are obtained from a straight line approximation to the curve over the stress range of interest. The use of tangent parameters does not infer that the shear strength is c’at zero effective normal stress.
- A straight line is drawn between a particular stress point and the origin or a line is drawn through the origin and tangential to a particular Mohr circle. The parameter c’ = 0 and the slope of the line gives Φ', the shear strength equation being
τf = tanf¢ σ'ftanΦ'.
The angle f¢ found Φ' found in this way is referred to as a secant parameter and is valid only for one particular stress state. The value of secant (f¢Φ') is generally the highest expected value of effective normal stress (i.e., the lowest value of the parameter for the stress range of interest).
Figure 1. Mohr-Coulomb Failure Criterion.
The relationship between the shear strength parameters and the effective principal stress at failure at a particular point can be deduced. The general case w/c’ > 0 is shown in Figure 1, compressive strength taken as positive. The coordinates of the tangent point are (τf,σ'f) where
τf = [(σ'1 – σ'3)sin(2θ)]/2, and
s¢f = [(s¢1 + s¢3)/2] + [(s¢1 – s¢3)cos(2q)]/2
andis the theoretical angle between the major principal plane and the plane of failure. The Mohr-Coulomb strength criterion is the combination Mohr failure envelope, approximated by linear intervals over certain stress ranges, and the Coulomb strength parameters.
Since
q = 45° + (q¢/2), and
sin(q¢) = [(s¢1 – s¢3)/2]/[c¢cot(q¢) + (s¢1 + s¢3)/2]; therefore,
(s¢1 – s¢3) = (s¢1 + s¢3)sin(q¢) + 2c¢cos(q¢), or
s¢1 = s¢3 tan2[45° + (q¢/2)] + 2c¢tan[45° + (q¢/2)].
This equation is known as the Mohr-Coulomb failure criterion.
When a material is sheared under a load or applied stress, excess pore water pressure is produced that may or may not escape depending on the permeability of the material and the time available.
In the undrained shear scenario, volume changes translate into pore pressure changes and the assumption is made that the pore pressure and therefore the effective stress (s¢ = s – u) are identical to those in the field. The total, or the undrained, shear strength is used for stress analysis. Tests must be conducted rapidly enough so that undrained conditions prevail if draining is possible in the experimental setup.
In the drained scenario, shear stress is used in terms of effective stresses. The excess hydrostatic pressure must be measured or estimated. Knowing the initial and the applied (total) stresses, the effective stress acting in the sediment can be calculated. This approach is philosophically more satisfying because pore water cannot carry any shear stress (i.e., shear strength is thought to be controlled by the effective stresses). Drained shear can ordinarily be determined only in the laboratory and the procedure is not popular because there are serious practical problems. Particularly in low-permeability material, the rate of loading must be sufficiently slow to avoid the development of excessive pore pressure, which can cause a test to take many days or weeks.
For a given state of stress it is apparent that, because s¢1 = s1 – u and s¢3 = s3 – u, the Mohr circles for total and effective stresses have the same diameter but their centers are separated by the corresponding pore water pressure u. Similarly, total and effective stress points are separated by the value of u.
The shear strength parameters for a particular soil can be determined by means of laboratory tests on specimens taken from representative samples of the in situ soil. These tests should only be used as guides because there are many reasons why the results are only approximate. Particularly, the influence of pore pressure changes during the undrained experiment cannot be estimated.
Sediment Strength Measurement
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