Shear Strength

Understanding Shear Strength

In soil mechanics, the term "shear strength" refers to the maximum shear stress that a soil can withstand. The resistance to shear is due to the friction and interlocking of particles, as well as any cementation or bonding between particles. When a particulate material is subject to shear strains, it may expand or contract in volume due to interlocking. If the volume expands, the density of the particles decreases, resulting in a decrease in strength. This reduction in strength follows the peak strength. The stress-strain relationship levels off when the material stops expanding or contracting, and when interparticle bonds are broken. At this point, the shear stress and density remain constant, and this state is known as the critical state, steady state, or residual strength. The volume change behavior and interparticle friction depend on several factors, such as particle density, intergranular contact forces, shearing rate, and the direction of the shear stress.

Effective stress refers to the average normal intergranular contact force per unit area. If water cannot flow in or out of the soil, the stress path is referred to as an undrained stress path. During undrained shear, if the particles are surrounded by an incompressible fluid, such as water, then the density of the particles cannot change without drainage, but the water pressure and effective stress will change. In contrast, if fluids are allowed to drain freely out of the pores, then the pore pressures remain constant, and the test path is called a drained stress path. The soil is free to expand or contract during shear if it is drained. In reality, soil is partially drained, falling between the perfectly undrained and drained idealized conditions.

The shear strength of soil depends on several factors, such as effective stress, drainage conditions, particle density, strain rate, and direction of strain. The Tresca theory is suitable for predicting the shear strength for undrained, constant volume shearing, while the Mohr-Coulomb theory is applicable for drained conditions.

Two important theories of soil shear are the critical state theory and the steady state theory. These theories differ in their assumptions and corresponding predictions.

Factors controlling shear strength

According to Poulos (1989), several factors affect the stress-strain relationship and shear strength of soils:

Composition

These factors include the basic soil material, which encompasses the mineralogy, grain size and distribution, shape of particles, and pore fluid type and content.

State

The initial state of the soil, described by the initial void ratio, effective normal stress, and shear stress, also plays a significant role.

Structure

The structure of the soil, such as layers, joints, fissures, slickensides, voids, pockets, and cementation, affects the stress-strain relationship as well.

Loading Conditions

Loading conditions, including the effective stress path (drained or undrained), loading type (magnitude, rate, and time history), also influence the soil's stress-strain behavior and shear strength.

Terms used to describe the soil's state and structure include loose, dense, overconsolidated, normally consolidated, stiff, soft, contractive, dilative, undisturbed, disturbed, remoulded, compacted, cemented, flocculent, honey-combed, single-grained, flocculated, deflocculated, stratified, layered, laminated, isotropic, and anisotropic.

Undrained Shear Strength

Undrained strength is a crucial concept in soil mechanics, which refers to the ability of a soil to resist deformation under undrained loading conditions. Unlike drained strength, which is the shear strength of a soil under fully drained conditions, undrained strength is influenced by various factors, including orientation of stresses, stress path, rate of shearing, and volume of material.

The undrained strength is typically defined by the Tresca theory, which states that the difference between the major and minor principal stresses (σ1-σ3) is twice the undrained strength (Su). This relationship is used in limit equilibrium analyses where the rate of loading is much greater than the rate at which pore water pressure dissipates. It is commonly observed in natural disasters, such as earthquakes or heavy rain, where rapid loading of sands or failure of clay slopes can lead to soil deformation.

One of the essential implications of the undrained condition is that no elastic volumetric strains occur, and thus Poisson's ratio is assumed to remain 0.5 throughout shearing. The Tresca soil model assumes no plastic volumetric strains occur, which is critical in advanced analysis methods such as finite element analysis. In these advanced analysis methods, other soil models such as Mohr-Coulomb and critical state soil models such as the modified Cam-clay model may be used to model the undrained condition.

Practising engineers frequently use the empirical observation that the ratio of the undrained shear strength (c) to the original consolidation stress (p') is roughly a constant for a given Over Consolidation Ratio (OCR). This relationship was formalized by Henkel in 1960 and further extended by Henkel and Wade in 1966, who showed that the stress-strain characteristics of remolded clays could also be normalized with respect to the original consolidation stress. This constant c/p relationship can also be derived from theory for both critical-state and steady-state soil mechanics. This fundamental normalization property of the stress-strain curves is found in many clays and has been refined into the empirical SHANSEP method by Ladd and Foott in 1974.

In summary, undrained strength is a critical concept in soil mechanics that describes a soil's ability to resist deformation under undrained loading conditions. Understanding the undrained strength of a soil is essential in various construction and engineering projects, and practitioners can use empirical relationships to estimate the undrained shear strength of a soil.

Drained Shear Strength

Drained shear strength is a fundamental concept in soil mechanics that describes a soil's ability to resist shearing forces while allowing for the dissipation of pore water pressure. This phenomenon occurs when pore water pressures generated during shearing can dissipate, or in soils where there is no pore water present. Engineers commonly approximate drained shear strength using the Mohr-Coulomb equation, which was originally called "Coulomb's equation" by Karl von Terzaghi in 1942. Terzaghi combined this equation with the principle of effective stress to better understand soil behavior.

The Mohr-Coulomb equation calculates the shear strength of a soil in terms of effective stresses, which are defined as the difference between the total stress applied normal to the shear plane and the pore water pressure acting on the same plane. The equation includes three main components: effective stress friction angle (φ'), cohesion (c'), and the coefficient of friction (μ). The effective stress friction angle represents the angle of internal friction, or the maximum angle at which a soil can resist shear forces without undergoing plastic deformation. The coefficient of friction is equal to the tangent of the effective stress friction angle. Cohesion is a measure of a soil's ability to resist shear forces without the need for frictional resistance. It is important to note that cohesion is a function of the range of stresses considered and is not a fundamental soil property.

Understanding the drained shear strength of soil is critical in various engineering applications. For instance, it plays a key role in slope stability analysis, where it helps determine the maximum angle at which a soil slope can remain stable. Drained shear strength is also essential in the design of foundations, retaining walls, and other geotechnical structures. By approximating a soil's drained shear strength, engineers can better predict how a soil will behave under different loading conditions and design structures that are both safe and cost-effective.

Critical State Theory

The critical state theory of soil mechanics, developed by Roscoe, Schofield, and Wroth in 1958, is based on a more advanced understanding of soil behavior under shearing. This theory identifies a distinct shear strength at which the soil undergoing shear maintains a constant volume, known as the critical state. In this state, there are three commonly identified shear strengths for a soil undergoing shear: peak strength, critical state or constant volume strength, and residual strength.

The peak strength may occur before or at the critical state, depending on the initial state of the soil particles undergoing shear force. Loose soils contract in volume on shearing and may not develop any peak strength above the critical state. Dense soils may contract slightly before granular interlock prevents further contraction. To continue shearing, the soil must dilate, resulting in a peak strength caused by dilation. Once this peak strength is overcome through continued shearing, the resistance provided by the soil to the applied shear stress decreases, termed "strain softening."

The constant volume shear strength, or critical state strength, is extrinsic to the soil and independent of the initial density or packing arrangement of the soil grains. In this state, the grains being separated are said to be "tumbling" over one another, with no significant granular interlock or sliding plane development affecting the resistance to shearing.

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). The critical state theory can be used in practice, but c' = 0 should be adopted, and the effects of potential rupture or strain softening to critical state strengths should be considered.

However, the critical state concept has been criticized for its inability to match readily available test data from testing a wide variety of soils. This is primarily due to its inability to account for particle structure, resulting in poor fits to volume and pore pressure change data. Additionally, critical state elasto-plastic models assume that elastic strains drive volumetric changes, which is not the case in real soils, further contributing to poor matches to empirical test data.

Steady state (dynamical systems based soil shear)

The concept of the critical state in soil mechanics has been refined into the steady state concept. The steady state strength refers to the shear strength of soil when it is in a condition of steady state. The steady state condition, as defined by Steve J. Poulos, is a state where the mass is continuously deforming at a constant volume, normal effective stress, shear stress, and velocity. This concept was built upon a hypothesis formulated by Arthur Casagrande towards the end of his career. Steady state based soil mechanics is sometimes referred to as "Harvard soil mechanics". It is important to note that the steady state condition is not the same as the critical state condition.

The steady state condition occurs only after all particle breakage, if any, is complete, and all particles are oriented in a statistically steady state condition so that the shear stress required to continue deformation at a constant velocity does not change. This condition applies to both the drained and undrained cases. The steady state has a slightly different value depending on the strain rate at which it is measured. While the steady state shear strength at the quasi-static strain rate may seem to correspond to the critical state shear strength, there is an additional difference between the two states. At the steady state condition, the grains position themselves in a steady state structure, whereas no such structure occurs for the critical state. For soils with elongated particles, the steady state structure is one where the grains are oriented in the direction of shear. In cases where the particles are strongly aligned in the direction of shear, the steady state corresponds to the "residual condition".

There are several common misconceptions regarding the steady state, including that it is the same as the critical state (it is not), that it applies only to the undrained case (it applies to all forms of drainage), and that it does not apply to sands (it applies to any granular material). A primer on the Steady State theory can be found in a report by Poulos, and its use in earthquake engineering is described in detail in another publication by Poulos.

It is important to note that the difference between the steady state and the critical state is not merely a matter of semantics. The strict definition of the steady state, which requires a constant deformation velocity and a statistically constant structure, places the steady state condition within the framework of dynamical systems theory. The use of this strict definition in describing soil shear as a dynamical system has been explored by Joseph. The underlying basis of the soil shear dynamical system is simple friction.