Vertical Stresses within Soils

1
Vertical Stresses within Soils

• Evaluation of Concentrated and Uniformly
  Distributed Loads for Pavement Design

2
Objectives

• Analyze incremental stress at a given point in
  the subsurface due to external load on soil

3
Pavement Design

• Types of pavement
• soil
• soil-cement
• asphalt (flexible) - multi-layered system
• concrete (rigid)

4
Shear Strength

• Coulomb Equation
• s c s tan f
• c 0 cohesionless soils (sand, gravel)
• f 0 cohesive soils (clay)
• Cohesion unconfined compressive strength
• c qu/2

5
Analysis of Vertical Pressure Beneath
Concentrated Load

• Approximate Method
• Elastic Theory
• Westergaard Equation (1938)
• alternating layers of elastic and nonelastic
  material
• Boussinesq Equation (1885)
• homogeneous, isotropic soil
• Influence Charts

6
Westergaard Theory

• q vertical stress increment at depth z this is
  in addition to prior stress (overburden pressure)
  
• Q concentrated load
• r horizontal distance from point of application
  of Q to the point at which q is desired
• m Poissons Ratio (strain normal to applied
  stress strain parallel to applied stress)

7
Westergaard Equation

• To simplify analysis, use Poissons Ratio (m)
  0, that is, if lateral strain 0 then no bulging
  of the soil occurs

8
Boussinesq Equation

• Generally, more widely used for analysis
• At low ratios of r/z, this will yield a greater
  vertical stress increment than Westergaards
  method

9
Example

• A concentrated 250 ton load is applied to the
  ground surface. Find the vertical stress
  increment
• at 20 feet below the load
• at 20 feet deep and 16 feet from the line of the
  load

10
Uniform LoadApproximate Method

• Simply assumes that the horizontal area of stress
  increases linearly with depth

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