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In modern soil mechanics, both these classical approaches (Tresca and Mohr–Coulomb) may be superseded by critical state theory or by steady state theory either of which can be considered in both undrained and drained terms and also cases involving partial drainage. The classical approaches are still in common usage though more progressive schools teach critical and/or steady state theory as part of an undergraduate civil engineering program. Consequently, they are also used in practice. Note that the critical state and stead state are two entirely different concepts.
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.
The shear strength of soils is taught in detail in specialist masters degree programs. Such programs usually include the use of modern numerical modeling techniques such as finite element analysis coupled with a model for shear strength such as critical state or stead state soil mechanics.
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The stressstrain relationship of soils, and therefore the shearing strength, is affected (Poulos 1989) by:
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:
Undrained strength is typically defined by Tresca theory, based on Mohr's circle as:
σ_{1}  σ_{3} = 2 S_{u}
Where:
σ_{1} is the major principal stress
σ_{3} is the minor principal stress
τ is the shear strength (σ_{1}  σ_{3})/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 in finite element analysis. In these advanced analysis methods, soil models other than Tresca may be used to model the undrained condition including MohrCoulomb and critical state soil models such as the modified Camclay model, provided Poisson's ratio is maintained at 0.5.
One relationship used extensively by practicing engineers is the empirical observation that the ratio of the undrained shear strength c to the effective confining stress p' is approximately a constant for a given Over Consolidation Ratio (OCR), and varies linearly with the logarithm of the OCR. This idea was extended to laboratory data in the empirical SHANSEP (stress history and normalized soil engineering properties) method.(Ladd & Foott 1974). This relationship can also be derived from both criticalstate and steadystate soil mechanics.
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 dissipate rapidly. It also applies where no pore water exists in the soil (the soil is dry). It is commonly defined using MohrCoulomb theory (it was called "Coulomb's equation" by Karl von Terzaghi in 1942 (Terzaghi 1942) 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 micromechanical 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.(Schofield 1998) 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,Heyman 1972 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 yintercept is nonzero. Some feel that this is not due to true cohesion, but is the effect of interlocking of particles.
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'.
A more advanced understanding of the behaviour of soil undergoing shearing lead to the development of the critical state theory of soil mechanics (Roscoe, Schofield & Wroth 1958). 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:
The peak strength may occur before or at critical state, depending on the initial state of the soil particles being sheared:
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 platelike minerals, but is also observed in some granular soils with more elongate shaped grains. Clays that do not have platelike 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).
The Critical State occurs at the quasistatic strain rate. It does not allow for differences in shear strength based on different strain rates. Also at the critical state, there is no particle alignment or specific soil structure.
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." (Poulos 1981) Steve Poulos built off a hypothesis that Arthur Casagrande was formulating towards the end of his career.(Poulos 1981) Steady state based soil mechanics is sometimes called "Harvard soil mechanics". It is not the same as the "critical state" condition.
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. It applies to both the drained and the undrained case.
The steady state has a slightly different value depending on the strain rate at which it is measured. Thus the steady state shear strength at the quasistatic strain rate (the strain rate at which the critical state is defined to occur at) would seem to correspond to the critical state shear strength. However there is an additional difference between the two states. This is that at the steady state condition the grains align in the direction of shear, whereas no such oriented structure occurs for the critical state. In this sense the steady state corresponds to the "residual" condition.
Harvard University's soil mechanics department shut down in 1970 after Casagrande retired but even today, the concept of the steady state condition remains powerfully relevant, a reflection of the stagnation of research in soil shear.
Two common misconceptions regarding the steady state are that a) it is the same as the critical state and b) that it applies only to the undrained case. A primer on the Steady State theory can be found in a report by Poulos (Poulos 1971). Its use in earthquake engineering is described in detail in another publication by Poulos (Poulos 1989).

