Shear strength (soil)

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Shear strength in reference to soil is a term used to describe the maximum strength of soil at which point significant plastic deformation or yielding occurs due to an applied shear stress. There is no definitive 'shear strength' of a soil, as it depends on a number of factors affecting the soil at any given time and on the frame of reference, in particular the rate at which the shearing occurs.

Two theories are commonly used to estimate the shear strength of a soil depending on the rate of shearing as a frame of reference. These are Tresca theory for short term loading of a soil, commonly referred to as the undrained strength or the total stress condition; and Mohr-Coulomb theory combined with the principle of effective stress for the long term loading of a soil, commonly referred to as the drained strength or the effective stress condition.

In modern soil mechanics, both these classical approaches (Tresca and Mohr-Coulomb) may be superseded by Critical State Theory, which can be considered in both undrained and drained terms, and also cases involving partial drainage. The classical approaches are still in common usage however, both as taught material in undergraduate civil engineering programmes, and consequently also in design codes of practice. Advanced soil mechanics is often taught in specialist Masters degree programs, and the pre-requesite to practice as a Geotechnical Engineer often requires such training, particularly with the use of modern numerical techniques in design such as Finite Element Analysis.

Contents 1 Undrained strength 2 Drained strength 3 Critical state strength 4 References

[edit] Undrained strength

This term describes a type of shear strength in soil mechanics as distinct from drained strength.

Conceptually, there is no such thing as the undrained strength of a soil. It depends on a number of factors, the main ones being:

• Orientation of stresses
• Stress path
• Rate of shearing
• Volume of material (like for fissured clays or rock mass)

Undrained strength is typically defined by Tresca theory, based on Mohr's Circle as:

σ₁ - σ₃ = 2 S_u

Where;

σ₁ = Major principal stress;

σ₃ = Minor principal stress;

& Shear strength τ = (σ₁ - σ₃)/2

hence; τ = S_u (or sometimes c_u) -the undrained strength.

It is commonly adopted in limit equilibrium analyses where the rate of loading is very much greater than the rate at which pore water pressures, that are generated due to the action of shearing the soil, may dissipate. An example of this is rapid loading of sands during an earthquake, or the failure of a clay slope during heavy rain, and applies to most failures that occur during construction.

As an implication of undrained condition, no elastic volumetric strains occur, and thus Poisson's ratio is assumed to remain 0.5 throughout shearing. The Tresca soil model also assumes no plastic volumetric strains occur. This is of significance in more advanced analyses such as the finite element analysis. In these advanced analysis methods, other soil models than Tresca may be used to model the undrained condition, including Mohr-Coulomb and critical state soil models such as the modified Cam-clay model, provided Poisson's ratio is maintained at 0.5.

[edit] Drained strength

This term describes a type of shear strength in soil mechanics as distinct from undrained strength.

The drained strength is the strength of the soil when pore water pressures, generated during the course of shearing the soil, are able to rapidly dissipate. It also applies where no pore water exists in the soil (the soil is dry). It is commonly defined using Mohr-Coulomb theory (It was called "Coulombs equation" by Terzaghi 1942^[1]), combined with the principle of effective stress.

Drained strength is defined as:

τ = σ' tan(φ') + c'

Where σ' =(σ - u), known as the principle of effective stress. σ is the total stress applied normal to the shear plane, and u is the pore water pressure acting on the same plane.

φ' = the effective angle of shearing resistance. Formerly termed 'angle of internal friction' after Coulomb friction, where the coefficient of friction μ is equal to tan(φ), which is proportional to the normal force on a plane but independent of its area. It is now regarded to have little to do with friction, and more to do with the micro-mechanical interaction of soil particles. Has sometimes been referred to as the 'angle of repose', as a dry granular material will form a pile at this angle, but no steeper. It is further described as either Peak φ'_p, Critical State φ'_cv or residual φ'_r. Note that φ'_p is only adopted in relation to Terzaghi's misunderstanding of the nature of "true" cohesion^[2]. Nowadays Critical State φ'_cv values should be prescribed.

c' = apparent cohesion. Allows the soil to possess some shear strength at no confining stress, or even under tensile stress. Commonly ascribed to temporary negative pore water pressures (suction), that dissipate over time. It may also be due to diagenetic affects caused by soil aging such as chemical bonding, cementation of grains and the effects of creep; indeed Coulomb identified that soil possessed no cohesion when newly remoulded ^[3], as these diagenetic effects had been destroyed. When shear tests are conducted on an overconsolidated or dense soil, and peak strengths are plotted on a τ/σ plot, it appears that cohesion exists as the y-intercept is non-zero. However, what is being plotted is not "true" cohesion, but is actually due to interlock of particles. This was first identified by Taylor (1948)^[4] for sands in tests carried out at MIT, and Roscoe, Schofield and Wroth (1968)^[5] at Cambridge explained the same effect for clays in terms of their Critical State Theory of soil mechanics. In any case, the long term loading condition must rely on the soil properties expected to exist and contribute to the shear strength of the soil over the long term, and for these reasons it is generally not considered a reliable soil mechanical property unlike φ'.

[edit] Critical state strength

A more advanced understanding of the behaviour of soil undergoing shearing has has lead to the development of the critical state theory of soil mechanics. In this theory, a distinct shear strength is identified where the soil undergoing shear does so at a constant volume, also called the 'critical state'. Thus there are three commonly identified shear strengths for a soil undergoing shear:

• Peak strength τ_p
• Critical state or constant volume strength τ_cv
• Residual strength τ_r

The peak strength may occur before or at critical state, depending on the initial state of the soil particles being sheared:

• A loose soil will contract in volume on shearing, and may not develop any peak strength above critical state. In this case 'peak' strength will coincide with the critical state shear strength, once the soil has ceased contracting in volume. It may be stated that such soils do not exhibit a distinct 'peak strength'.
• A dense soil may contract slightly before granular interlock prevents further contraction (granular interlock is dependent on the shape of the grains and their initial packing arrangement). In order to continue shearing once granular interlock has occurred, the soil must dilate (expand in volume). As additional shear force is required to dilate the soil, a 'peak' strength occurs. Once this peak strength caused by dilation has been overcome through continued shearing, the resistance provided by the soil to the applied shear stress reduces (termed "strain softening"). Strain softening will continue until no further changes in volume of the soil occur on continued shearing. Peak strengths are also observed in overconsolidated clays where the natural fabric of the soil must be destroyed prior to reaching constant volume shearing. Other affects that result in peak strengths include cementation and bonding of grains.

The constant volume (or critical state) shear strength is said to be intrinsic to the soil, and independent of the initial density or packing arrangement of the soil grains. In this state the grains being sheared are said to be 'tumbling' over one another, with no significant granular interlock or sliding plane development affecting the resistance to shearing. At this point, no inherited fabric or bonding of the soil grains affects the soil strength.

The residual strength occurs for some soils where the shape of the particles that make up the soil become aligned during shearing (forming a slickenside), resulting in reduced resistance to continued shearing (further strain softening). This is particularly true for most clays that comprise plate-like minerals, but is also observed in some granular soils with more elongate shaped grains. Clays that do not have plate-like minerals (like allophanic clays) do not tend to exhibit residual strengths.

Use in practice: If one is to adopt Critical State Theory, and take c' =0; τ_p may be used, provided the level of anticipated strains are taken into account, and the effects of potential rupture or strain softening to critical state strengths are considered. For large strain deformation, the potential to form slickensided surface with a φ'_r should be considered (such as pile driving).

[edit] References