SHEAR STRENGTH (SOIL)

'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In modern soil mechanics, both these classical approaches (Tresca and Mohr-Coulomb) may be superseded by critical state theory which can be considered in both undrained and drained terms and also cases involving partial drainage.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 are taught in undergraduate civil engineering programmes, and consequently, they are also used in practice.
Shear strength of a soil is also of importance in designing for earthquakes where the concept of the soil's steady state shear strength is used.
Advanced soil mechanics is often taught in specialist masters degree programs, and the prerequisite to practice as a geotechnical engineer often requires such training, particularly with the use of modern numerical techniques such as finite element analysis and with the adoption of critical state soil models.

Contents

Factors Controlling Shear Strength of Soils

Undrained strength

Drained strength

Critical state strength

Steady state strength

Notes

References

Factors Controlling Shear Strength of Soils

The stress-strain relationship of soils, and therefore the shearing strength, is affected by ^[1]:
# 'soil composition (basic soil material)': mineralogy, grain size and grain size distribution, shape of particles, pore fluid type and content, ions on grain and in pore fluid.
# 'state (initial)': Define by the initial void ratio, effective normal stress and shear stress (stress history). State can be describe by terms such as: loose, dense, overconsolidated, normally consolidated, stiff, soft, contractive, dilative, etc.
# 'structure:' Refers to the arrangement of particles within the soil mass; the manner the particles are packed or distributed. Features such as layers, joints, fissures, slickensides, voids, pockets, cementation, etc, are part of the structure. Structure of soils is described by terms such as: undisturbed, disturbed, remolded, compacted, cemented; flocculent, honey-combed, single-grained; flocculated, deflocculated; stratified, layered, laminated; isotropic and anisotropic.
# 'Loading conditions:' Effective stress path, i.e., drained, and undrained; and type of loading, i.e., magnitude, rate (static, dynamic), and time history (monotonic, cyclic)).

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'' is the major principal stress
''σ₃'' is the minor principal stress
$au$ is the shear strength ''(σ₁ - σ₃)/2''
hence, $au$ = ''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 in finite element analysis. In these advanced analysis methods, soil models other 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.
One important empirical relationship used extensively by practicing engineers is the empirical SHANSEP relationship.^[2] This is based on the observation that the logarithm of the undrained shear strength S_u normalized by the vertical consolidation stress σ_vc plots linearly against the logarithm of the over consolidation ratio or OCR, that is, S_u/σ_vc=K
★ OCR^N where K and N are constants that depend on the soil and the loading used to shear the soil. To date, no physical model has been proposed that explains this empirical observation.

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 Karl Terzaghi in 1942^[2]) combined with the principle of effective stress.
Drained strength is defined as:
$au$ = ''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 $mu$ 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. It 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.^[4] 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,^[2] 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 $au$/$sigma$ plot, it appears that cohesion exists as the y-intercept is non-zero. However, what is being plotted is not "true" cohesion, but it is actually due to interlock of particles in the case of sands and inter-particle attractive forces in the case of clays. This was first identified by Taylor (1948)^[2] for sands in tests carried out at MIT, and for clays by Roscoe, Schofield and Wroth (1958) at Cambridge. This paper by Roscoe et al. is considered a landmark in soil mechanics and forms the basis of 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'.

Critical state strength

A more advanced understanding of the behaviour of soil undergoing shearing lead to the development of the critical state theory of soil mechanics. This understanding was largely based on the work of Kenneth Harry Roscoe of Cambridge University, in the late forties and early fifties. Roscoe published his work as the senior author of the paper that laid down basis of critical state theory. Roscoe obtained his undergraduate degree in mechanical engineering^[7] and his exposure to the metal failure theories of his day may have influenced his approach to soil shear.
In critical state soil mechanics, 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 $au$_p

★ Critical state or constant volume strength $au$_cv

★ Residual strength $au$_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 particles.
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. Note that there is no restriction on the strain-rate needing to be a constant and this distinguishes the critical state shear strength from the soil's steady state shear 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; $au$_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).
In recent years, critical state soil mechanics appears to have reached a dead end. For example, it has been unable to explain the emperical SHANSEP relationship. It may be that a theory which ignores soil structure is essentially limited in what it can explain.

Steady state strength

The steady state strength is defined as the shear strength of the soil when it is at the steady state condition. The steady state condition is defined as "that state in which the mass is continuously deforming at constant volume, constant normal effective stress, constant shear stress, and constant velocity." Steve Poulos built off a hypothesis that Arthur Casagrande was formulating towards the end of his career.
The steady state occurs only after all particle breakage if any is complete and all the particles are oriented in a statistically steady state condition and so that the shear stress needed to continue deformation at a constant velocity of deformation does not change.
The steady state is different from the critical state in that there is an additional requirement that the velocity of deformation must also be constant. It applies to both the drained condition (where it is colloquially referred to as the "residual strength") and to the undrained condition. Geotechnical engineers use the steady state shear strength when designing for earthquakes.

Notes

1. Poulos, S. J. 1989. Advance Dam Engineering for Design, Construction, and Rehabilitation: Liquefaction Related Phenomena. Ed. Jansen, R.B, Van Nostrand Reinhold, pages 292-297.
2.
3.
4. Schofield, A.N. 1998. ''The "Mohr-Coulomb" Error'', Mechanics and Geotechnique, Luong (ed.) LMS Ecole Polytechnique:19-27
Also: Technical Report No. 305, Cambridge University Engineering Dept. Dev. D Soil Mech. Gp. [1]
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7. Oxford Dictionary of National Biography, 1961-1970, entry on Roscoe, Kenneth Harry, pp 894-896

References

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