🏔️Intro to Geotechnical Science Unit 7 – Soil Shear Strength

Key Concepts and Definitions

• Shear strength represents the maximum shear stress a soil can withstand before failure occurs
• Cohesion ($c$) measures the soil's intrinsic shear strength due to electrostatic forces between particles
• Friction angle ($\phi$) quantifies the soil's frictional resistance to shearing, dependent on the normal stress
  • Typically ranges from 0° (very loose sand) to 45° (dense sand or gravel)
• Effective stress ($\sigma'$) accounts for the stress carried by the soil skeleton, equal to total stress minus pore water pressure
• Mohr-Coulomb failure criterion relates shear strength to normal stress, cohesion, and friction angle: $\tau = c + \sigma'\tan\phi$
• Drained conditions allow pore water to dissipate during loading, while undrained conditions prevent pore water dissipation
• Critical state soil mechanics describes the behavior of soil at large strains, where it continues to deform without changes in stress or volume

Soil Composition and Properties

• Soil consists of solid particles (sand, silt, clay), water, and air voids
• Particle size distribution (gradation) influences soil behavior and shear strength
  • Well-graded soils have a wide range of particle sizes, leading to higher density and shear strength
  • Poorly-graded soils have a narrow range of particle sizes, resulting in lower density and shear strength
• Plasticity index (PI) measures the range of water contents where clay exhibits plastic behavior
• Void ratio ($e$) represents the ratio of void volume to solid volume in a soil sample
• Relative density ($D_r$) expresses the degree of compaction for granular soils, affecting shear strength and stiffness
• Soil structure refers to the arrangement of particles and pores, impacting strength and permeability
  • Flocculated structure (clay particles in edge-to-face contact) leads to higher void ratios and lower shear strength
  • Dispersed structure (clay particles in face-to-face contact) results in lower void ratios and higher shear strength

Stress in Soils

• Total stress ($\sigma$) is the sum of effective stress ($\sigma'$) and pore water pressure ($u$): $\sigma = \sigma' + u$
• Effective stress governs soil behavior and shear strength, as it represents the stress carried by the soil skeleton
• Pore water pressure develops in saturated soils under undrained loading, reducing effective stress and shear strength
• Overburden stress increases with depth due to the weight of overlying soil layers
• Lateral earth pressure is the horizontal stress acting on soil elements, influenced by soil properties and loading conditions
  • At-rest earth pressure ($K_0$) occurs when no lateral strain is allowed (retaining walls)
  • Active earth pressure ($K_a$) develops when soil is allowed to expand laterally (excavations)
  • Passive earth pressure ($K_p$) mobilizes when soil is forced to compress laterally (pile foundations)
• Shear stress ($\tau$) acts parallel to the soil element faces, causing angular distortion and shear deformation

Shear Strength Theory

• Mohr-Coulomb failure criterion defines the shear strength envelope in terms of cohesion and friction angle
• Peak shear strength is the maximum shear stress a soil can sustain before failure, corresponding to the peak of the stress-strain curve
• Residual shear strength is the minimum shear strength reached after large displacements, important for slope stability analysis
• Dilation occurs in dense granular soils, where particles must climb over each other during shearing, leading to volume increase
• Contraction happens in loose granular soils, where particles collapse into void spaces during shearing, resulting in volume decrease
• Critical state is reached when soil continues to deform at constant stress and volume, representing the ultimate shear strength
• Strain softening describes the reduction in shear strength after the peak, common in overconsolidated clays
• Strain hardening refers to the increase in shear strength with increasing strain, typical of normally consolidated clays

Testing Methods

• Direct shear test applies a normal stress and measures the shear force required to cause failure along a predetermined plane
  • Suitable for granular soils and quick estimates of shear strength parameters
  • Limited control over drainage conditions and stress path
• Triaxial compression test confines a cylindrical soil sample in a pressurized cell and applies axial load until failure
  • Allows control over drainage conditions (drained, undrained) and stress path (compression, extension)
  • Provides more reliable and representative shear strength parameters
• Unconfined compression test applies axial load to an unconfined cylindrical soil sample until failure, measuring the unconfined compressive strength
  • Used for quick estimates of shear strength in cohesive soils (clays)
  • Not suitable for granular soils or soils with significant confining stresses
• Vane shear test measures the in-situ undrained shear strength of soft clays by rotating a vane and measuring the torque at failure
  • Provides a quick and direct measurement of undrained shear strength
  • Limited to soft, saturated, cohesive soils
• Cone penetration test (CPT) pushes a instrumented cone into the soil, measuring tip resistance and sleeve friction
  • Provides continuous profiles of soil strength and behavior with depth
  • Correlations available to estimate shear strength parameters from CPT data

Factors Affecting Soil Shear Strength

• Soil type and mineralogy influence intrinsic shear strength properties (cohesion, friction angle)
  • Granular soils (sands, gravels) derive shear strength primarily from friction and interlocking
  • Cohesive soils (clays) exhibit shear strength due to electrostatic forces and cohesion
• Density and void ratio affect the shear strength of granular soils, with denser soils having higher strength
• Water content impacts the shear strength of cohesive soils, with increasing water content leading to reduced strength
• Confining stress increases the frictional component of shear strength in granular soils
• Drainage conditions during loading determine the development of pore water pressures and effective stresses
  • Drained loading allows dissipation of excess pore water pressures, maintaining effective stresses
  • Undrained loading generates excess pore water pressures, reducing effective stresses and shear strength
• Stress history and overconsolidation ratio (OCR) influence the shear strength and stiffness of cohesive soils
  • Overconsolidated soils (OCR > 1) exhibit higher shear strength and brittleness
  • Normally consolidated soils (OCR = 1) display lower shear strength and ductility
• Anisotropy results in different shear strengths depending on the direction of loading relative to the soil fabric

Real-World Applications

• Slope stability analysis assesses the risk of landslides and designs safe slopes using shear strength parameters
  • Factor of safety (FoS) compares the available shear strength to the shear stresses driving failure
  • Limit equilibrium methods (Bishop, Janbu, Spencer) calculate FoS for potential failure surfaces
• Foundation design relies on shear strength to ensure adequate bearing capacity and limit settlements
  • Shallow foundations (spread footings, mats) transfer loads to the soil near the surface
  • Deep foundations (piles, drilled shafts) transfer loads to stronger soil or rock layers at depth
• Retaining wall design uses shear strength to calculate lateral earth pressures and ensure stability against overturning and sliding
  • Gravity walls resist lateral pressures through their own weight and friction at the base
  • Cantilever walls consist of a vertical stem and base slab, using the soil's passive resistance for stability
• Excavation support systems (bracing, tieback anchors) rely on shear strength to maintain stability and prevent collapse
• Soil liquefaction assessment predicts the loss of shear strength in saturated, loose sands during earthquakes
  • Cyclic shear stresses can cause a rapid increase in pore water pressure, leading to a temporary loss of strength
  • Liquefaction potential is evaluated using in-situ tests (SPT, CPT) and laboratory cyclic shear tests

Common Challenges and Solutions

• Sample disturbance during collection and preparation can alter soil structure and lead to underestimated shear strengths
  • Minimize disturbance by using thin-walled samplers and careful handling techniques
  • Use in-situ tests (CPT, vane shear) to measure shear strength directly in the field
• Spatial variability of soil properties can result in uncertainty and potential failures
  • Conduct thorough site investigations with sufficient sampling and testing locations
  • Use geostatistical methods (kriging) to interpolate soil properties between data points
• Strain incompatibility between laboratory tests and field conditions can lead to overestimated or underestimated shear strengths
  • Select appropriate strain rates and stress paths in laboratory tests to mimic field conditions
  • Use back-analysis of case histories to calibrate shear strength parameters
• Time-dependent behavior (creep, consolidation) can cause long-term deformations and strength changes
  • Conduct long-term oedometer tests to assess consolidation and secondary compression
  • Use time-dependent constitutive models (modified Cam Clay, viscoelastic) in numerical simulations
• Multiphase interactions between solid particles, water, and air can complicate shear strength behavior
  • Use coupled hydro-mechanical models (Biot theory) to capture the interaction between pore fluids and soil skeleton
  • Consider unsaturated soil mechanics principles for soils above the water table
• Environmental factors (temperature, chemistry) can degrade soil shear strength over time
  • Assess the impact of temperature fluctuations on soil properties, especially in cold regions
  • Evaluate the potential for chemical reactions (dissolution, precipitation) that may alter soil structure and strength