CIVL2410 Chap.14 Shear strength, triaxial testing and critical states
Shear strength, triaxial testing and critical states
Soils are frictional, so their strength is not a single number: it rises with the effective stress holding the grains together and vanishes if pore pressure removes that stress.
This chapter sets out the failure criterion with both of the warnings the unit attaches to it, separates drained from undrained strength and matches each to its own stresses, describes the apparatus that measures them, and closes with the state every soil reaches at large strain.
What this chapter covers
- 01
Four forms of soil failure, and why they are one phenomenon
- 02
Mohr's circle as the complete state of stress at a point
- 03
The Mohr-Coulomb envelope, and what its intercept and slope represent
- 04
Why the two parameters are not soil constants
- 05
Why the criterion is empirical and only locally linear
- 06
Drained strength with effective parameters against undrained strength with total ones
- 07
Why the undrained friction angle is usually zero for a saturated clay
- 08
The shear box: what it knows, and what it cannot know
- 09
The triaxial cell, deviator stress, and drainage as a controlled variable
- 10
Unconsolidated undrained and consolidated undrained procedures
- 11
Relative density, dilatancy, and the peak a dense sand shows
- 12
The critical state, and why its friction angle is the one used for large movements
Cell pressure recovered from an undrained strength
- +1Undrained strength is the radius of the Mohr circle, and subtracting the pore pressure shifts the circle without resizing it, so the effective principal stress difference is 2 x 24 = 48 kPa.
- +1The failure condition with no cohesion is sigma1 prime = N phi times sigma3 prime.
- +1N phi = (1 + sin 28) / (1 - sin 28) = 1.469 / 0.531 = 2.77.
- +1Substituting: 2.77 sigma3 prime minus sigma3 prime = 48, so sigma3 prime = 48 / 1.77 = 27.1 kPa.
- +1The cell pressure is a total stress, so add the pore pressure back: 27.1 + 38 = 65 kPa.
Key terms
- Mohr-Coulomb criterion
- The failure condition in which shear strength is a cohesion intercept plus a friction term proportional to effective normal stress. It is an empirical straight line fitted to a curved failure locus.
- Undrained shear strength
- The single strength a saturated clay shows when loaded with no drainage, used with total stresses. It depends on the moisture content rather than on the applied confining pressure.
- Deviator stress
- The difference between the axial and radial stresses in a triaxial test, which is what has to be increased to cause failure once the cell pressure is set.
- Dilatancy
- The volume increase a dense soil shows when sheared, as grains ride over one another. It supplies the extra strength a dense specimen shows at peak, and it is spent by the time the critical state is reached.
- Critical state line
- The locus of the states soils reach at large strain, each defined by a unique stress ratio and a void ratio uniquely related to the normal stress.
Shear strength, triaxial testing and critical states FAQ
Why is the undrained friction angle usually reported as zero?
Run several undrained tests on saturated specimens of one clay at different cell pressures. Raising the cell pressure with no drainage raises the pore pressure by the same amount, so the effective stresses do not change and neither does the strength. Every specimen therefore fails at the same deviator stress, the total stress envelope comes out horizontal, and the friction angle is zero.
A non zero value is a signal to check the specimens rather than a result to use: it usually means they were not fully saturated, or that they were at different moisture contents and so were not really the same material.
Which friction angle should a design use?
For anything that must tolerate large movements, the critical state value. The peak friction angle a dense specimen shows is bought by dilatancy and is a property of the initial packing, so any mechanism that strains the soil substantially, such as a developing slip surface, will have passed the peak and be operating at the critical state by the time movement is noticeable.
The critical state angle depends on mineralogy, grading and angularity rather than on density, which is what makes it a property of the material.
Why is the triaxial cell preferred to the shear box?
Because of what each apparatus can know. A shear box reads forces and displacements but not their distribution over the shearing surface, which is not uniform, so stresses and strains cannot be recovered with confidence, and the failure plane is fixed by the apparatus rather than chosen by the specimen.
The triaxial cell keeps the stress state reasonably uniform, lets the specimen fail where it wants to, and above all allows drainage to be controlled and pore pressure to be measured, which is what makes effective stress parameters obtainable at all.
Exam move
Settle the drainage condition before anything else, because it decides which pair of parameters applies and which stresses they go with, and no later step can repair a wrong choice. Learn the algebraic form of the failure condition rather than working geometrically off the circle each time, since most triaxial questions become two lines once the drainage condition is fixed.
Attach both of the unit's warnings to any parameter you quote: that the values depend on the initial state and the loading type, and that the straight envelope is only reliable over the stress range it was fitted in. For the sand material, learn the four observations at equal mean effective stress as a single story rather than as separate facts, because the critical state is what ties them together.
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