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. For other uses, see Plasticity. ... Yield strength, or the yield point, is defined in engineering and materials science as the stress at which a material begins to plastically deform. ... Shear stress is a stress state where the stress is parallel to a face of the material, as opposed to normal stress when the stress is perpendicular to the face. ...

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. Henri Tresca (1814–1884) was French Mechanical Engineer, professor of Conservatoire National des Arts et Métiers in Paris. ... Mohr-Coulomb Theory is a mathematical model describing the response of rubble piles to the shear forces produced by gravity. ... Effective stress (σ) is a value reflecting the strength of a soil. ...

Undrained strength

This term describes a type of shear strength in soil mechanics as distinct from drained strength. Soil mechanics is a discipline that applies the principles of engineering mechanics to soil to predict the mechanical behavior of soil. ...

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: Stress is the internal distribution of force per unit area that balances and reacts to external loads applied to a body. ...

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. Elasticity is a branch of physics which studies the properties of elastic materials. ... This article is about the deformation of materials. ... Figure 1: Rectangular specimen subject to compression, with Poissons ratio circa 0. ... Visualization of how a car deforms in an asymmetrical crash using finite element analysis. ... Yield surface is described in three dimensional space of principal stresses (), and encompasses the elastic region of material behavior. ... Yield surface is described in three dimensional space of principal stresses (), and encompasses the elastic region of material behavior. ...

Drained strength

This term describes a type of shear strength in soil mechanics as distinct from undrained strength. Soil mechanics is a discipline that applies the principles of engineering mechanics to soil to predict the mechanical behavior of soil. ...

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, 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, 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'. Portrait of Coulomb Charles Augustin Coulomb (June 14, 1736 – August 23, 1806) was a French physicist. ... Friction is the force that opposes the relative motion or tendency toward such motion of two surfaces in contact. ... Angle of Repose is a 1971 novel by Wallace Stegner about a wheelchair bound historian, Lyman Ward, who has lost connection with his son and living family and decides to write about his frontier era grandparents. ...

c' = apparent cohesion. Allows the soil to possess some shear strength at no confining stress, or even 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 and cementation of grains, or when a shear test is conducted that is not strictly 'drained'; it may merely appear that the soil has some 'cohesion'. 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'. Mercury sticks together because of the cohesive forces. ... Tensile stress (or tension) is the stress state leading to expansion; that is, the length of a material tends to increase in the tensile direction. ... Suction is the creation of a partial vacuum, or region of low pressure. ... In geology and oceanography, diagenesis is any chemical, physical, or biological change undergone by a sediment after its initial deposition and during and after its lithification, exclusive of surface alteration (weathering) and metamorphism. ... In geology, cementation is the process of deposition of dissolved mineral components in the interstices of sediments. ...

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
• Critical state or constant volume strength
• Residual strength

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 dependant 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, 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.