7.1 Mohr-Coulomb failure criterion
4 min read•august 16, 2024
Soil is crucial in geotechnical engineering. It determines how much stress soil can handle before failing. This concept is key for designing stable structures like foundations and slopes.
The helps us understand when soil will fail under stress. It considers both and friction between soil particles. This model is widely used to predict soil behavior in various engineering applications.
Shear Strength in Geotechnical Engineering
Fundamentals of Shear Strength
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- Shear strength represents the internal resistance of soil to deformation by
- Defines the maximum shear stress a soil can withstand before failure occurs
- Critical parameter in geotechnical engineering influences stability of structures (foundations, slopes, retaining walls)
- Composed of two main components
- Cohesion (c)
- Internal friction (φ)
- Varies depending on soil type and conditions
Factors Influencing Shear Strength
- Soil composition affects shear strength (clay minerals, organic content)
- Particle size distribution impacts strength (well-graded vs poorly-graded soils)
- alters strength characteristics (dry vs saturated conditions)
- Density plays a role in strength development (loose vs dense states)
- Stress history influences behavior (normally consolidated vs overconsolidated soils)
- concept accounts for pore water pressure effects
- Total stress = effective stress + pore water pressure
- Effective stress governs soil strength and deformation
Measurement and Application
- Laboratory tests determine shear strength parameters
- Direct shear test measures strength along a predetermined failure plane
- Triaxial compression test allows for controlled drainage conditions
- Field tests provide in-situ strength measurements (vane shear test, cone penetration test)
- Understanding shear strength enables
- Prediction of soil behavior under loading
- Design of safe, stable geotechnical structures (retaining walls, foundations)
- Assessment of slope stability and landslide potential
Mohr-Coulomb Failure Envelope
Components and Representation
- Graphical representation of soil shear strength
- (σ) plotted on x-axis
- Shear stress (τ) plotted on y-axis
- Typically represented as a straight line
- Described by equation
- Cohesion (c) appears as y-intercept
- Represents inherent shear strength with no normal stress applied
- Friction angle (φ) determines slope of
- Represents angle of internal friction between soil particles
- Separates stress states causing failure (above line) from stable states (below line)
Variations in Failure Envelope
- Cohesionless soils (clean sands) have failure envelope passing through origin
- Indicates zero cohesion
- Shape and position change with soil properties
- Density affects slope (higher density increases friction angle)
- Moisture content alters cohesion (saturation generally reduces cohesion)
- Curved failure envelopes occur in some soils
- Reflects non-linear strength behavior at high stresses
- Residual strength envelope lies below peak strength envelope
- Represents reduced strength after large displacements
Applying the Mohr-Coulomb Criterion
Mathematical Expression and Parameters
- Mohr-Coulomb failure criterion expressed as
- τf represents shear strength at failure
- σf denotes normal stress at failure
- Determine cohesion (c) and friction angle (φ) through
- Laboratory testing (direct shear, triaxial tests)
- Empirical correlations based on soil classification
- Calculate maximum sustainable shear stress for given normal stress
- Applicable to both total stress and effective stress analyses
- Use appropriate parameters for each case (c', φ' for effective stress)
Applications in Geotechnical Engineering
- Analyze stability problems in various scenarios
- Slope stability assessment (factor of safety calculations)
- Retaining wall design (active and passive earth pressures)
- Foundation bearing capacity evaluation
- Undrained conditions for cohesive soils often assume φ = 0°
- Simplifies equation to τf = cu (undrained shear strength)
- Used in numerical modeling of soil behavior (finite element analysis)
- Guides selection of soil improvement techniques
- Increase density to enhance friction angle
- Add cementing agents to improve cohesion
Limitations and Considerations
- Linear approximation may not capture all soil behaviors
- Non-linear strength envelopes at high stresses
- Stress-dependent friction angles in some soils
- Does not account for intermediate principal stress effects
- Can lead to conservative estimates in some cases
- Time-dependent behavior not directly addressed
- Creep and relaxation may require additional considerations
- Anisotropy effects may necessitate different strength parameters in various directions
Normal vs Shear Stress at Failure
Relationship and Visualization
- Mohr-Coulomb model establishes linear relationship between normal and shear stress at failure
- Slope of relationship defined by friction angle (φ)
- Normal stress increase leads to higher shear stress required for failure
- Reflects frictional nature of soil behavior
- Cohesion intercept represents stress-independent strength contribution
- Particularly significant in cohesive soils (clays)
- Mohr circles represent stress states
- Failure envelope tangent to circles at critical stress combinations
- Failure occurs along plane inclined at angle of (45° + φ/2) to major principal stress direction
Advanced Analysis Techniques
- Stress path analysis predicts soil behavior under complex loading
- Useful for simulating construction sequences
- Helps understand stress history effects
- Critical state soil mechanics incorporates volume change behavior
- Defines unique relationship between void ratio and stress at large strains
- Strain rate effects can modify strength parameters
- Faster loading generally increases apparent strength
- Soil anisotropy may require different strength parameters in various directions
- Bedded deposits often exhibit directional strength variations
- Stress history influences strength characteristics
- Overconsolidation ratio affects both cohesion and friction angle
Key Terms to Review (18)
Bearing capacity assessment: Bearing capacity assessment refers to the evaluation of the ability of soil to support the loads applied to it without experiencing failure or excessive settlement. This assessment is crucial in geotechnical engineering as it helps determine the safe load that can be placed on a foundation, taking into account the soil's properties and the stress distribution caused by the load. Understanding this concept ensures that structures are built on stable ground and can support their intended use.
Brittle failure: Brittle failure is a mode of material fracture characterized by sudden and catastrophic breakage with little to no deformation prior to failure. This type of failure occurs when a material cannot absorb significant energy before it breaks, typically seen in materials that are stiff and exhibit high strength but low ductility. Understanding brittle failure is crucial for assessing the stability and safety of structures under load.
Charles-Augustin de Coulomb: Charles-Augustin de Coulomb was a French physicist and engineer best known for his work in the fields of electrostatics and mechanics, particularly in relation to the understanding of soil mechanics and friction. His contributions laid the groundwork for the Mohr-Coulomb failure criterion, which is essential for analyzing the shear strength of materials like soil and rock under stress conditions.
Cohesion: Cohesion is the property of soil that describes the attraction between soil particles, which contributes to the soil's strength and stability. This internal binding force is essential in understanding how soil behaves under different conditions, including how it interacts with moisture, external loads, and other forces acting on it.
Compaction: Compaction is the process of densifying soil by reducing the volume of air within its voids through mechanical means, thereby increasing its density and strength. This process plays a critical role in geotechnical engineering by enhancing soil properties, reducing settlement, and improving load-bearing capacity.
Ductile failure: Ductile failure is a mode of material failure characterized by significant plastic deformation before fracture. This type of failure indicates that a material can undergo substantial elongation or deformation, which allows for energy absorption and redistribution of stress, rather than breaking suddenly. Understanding ductile failure is crucial for analyzing the stability and safety of structures under load conditions.
Effective Stress: Effective stress is the stress that contributes to the strength and stability of soil, representing the difference between total stress and pore water pressure within the soil. This concept is crucial in understanding how soil behaves under various conditions, particularly in the context of fluid movement, consolidation, and strength properties of soils.
Failure envelope: A failure envelope is a graphical representation that defines the limits of strength for materials under various conditions of stress, particularly in soil mechanics. It illustrates how a material will fail when subjected to different combinations of normal and shear stresses, helping engineers understand the stability and safety of soil structures.
Internal friction angle: The internal friction angle is a measure of the shear strength of granular materials, reflecting the resistance of particles to sliding past one another under load. This angle plays a crucial role in understanding soil mechanics, influencing the stability of slopes and the design of foundations. It is represented as the angle at which the shear strength of soil can overcome gravitational forces acting on it, impacting various engineering applications.
Karl von Terzaghi: Karl von Terzaghi was an Austrian civil engineer and geologist known as the father of soil mechanics. He significantly advanced the understanding of the behavior of soils under load, establishing fundamental concepts that underpin modern geotechnical engineering, particularly the Mohr-Coulomb failure criterion which describes how materials fail under shear stress.
Mohr Circle: Mohr Circle is a graphical representation used in engineering and geology to visualize the relationship between normal and shear stresses on different planes within a material. It serves as a powerful tool for understanding the stress state at a point, enabling engineers to determine how materials will behave under various loading conditions, particularly in the context of failure criteria like the Mohr-Coulomb failure criterion.
Mohr-Coulomb Failure Criterion: The Mohr-Coulomb failure criterion is a mathematical model that describes the shear strength of soil and other materials based on their internal friction and cohesion. This criterion helps engineers predict when materials will fail under stress by relating shear strength to normal stress through a linear relationship defined by the cohesion intercept and the angle of internal friction.
Moisture Content: Moisture content refers to the amount of water present in a soil sample, expressed as a percentage of the dry weight of the soil. It plays a crucial role in understanding soil behavior and properties, influencing the results of site investigations, strength assessments, and stability analyses. Knowing the moisture content helps in determining the effective stress within the soil and is essential for accurate engineering applications.
Normal stress: Normal stress is the force per unit area acting perpendicular to a surface, typically resulting from external loads applied to soil. It plays a crucial role in understanding how soil responds to these loads, affecting stability and the potential for failure. By analyzing normal stress, engineers can predict how soil will behave under various conditions, which is essential for safe construction and land use.
Shear Strength: Shear strength is the maximum resistance of a soil or rock to shear stress, which is critical in understanding how materials behave under loading conditions. This concept is essential in various aspects of geotechnical engineering, as it influences stability, load-bearing capacity, and the overall performance of structures in contact with soil.
Shear Stress: Shear stress is the force per unit area exerted parallel to the surface of a material, causing it to deform or slide. In geotechnical science, understanding shear stress is crucial because it helps assess how soils respond to external loads and how they distribute stress across different layers, which directly relates to their strength and stability.
Slope stability analysis: Slope stability analysis is a method used to determine the safety and stability of slopes, assessing the potential for landslides or other failures due to gravitational forces acting on soil and rock materials. This analysis incorporates various factors such as the effective stress within the slope, external loads, and material properties to predict whether a slope will remain stable or if it is at risk of failure under certain conditions.
τ = c + σ tan φ: The equation τ = c + σ tan φ represents the Mohr-Coulomb failure criterion, which is used to describe the shear strength of materials, particularly soils and rocks. In this equation, τ is the shear strength, c is the cohesion, σ is the normal stress acting on the failure plane, and φ is the angle of internal friction. This relationship helps predict when a material will fail under applied stress, providing crucial insights into stability and failure mechanisms in geotechnical engineering.