[L12] Stresses in soils

Soil-structure interaction

development + construction of infrastructure alters the state of soils

Man-made embankment composition example

1. Overburden

2. Pindan scree B

3. Sapprolitic clays

4. Shale

(from top to bottom)

Pressure

• scalar quantity = single parameter

• same in all directions

Stress

• not a scalar quantity ➞ more than 1 parameter

• direction-dependent ➞ diff magnitudes of normal stress in vertical & horizontal

Hydrostatic water pressure (w/ no flow)

• scalar

• same in all directions

• water ➞ cannot sustain shear forces, incompressible

• water density (rho_w)= 1000 kg/m3

• water pressure (u)

u=rho_w*g*z=𝛾_w*z (specific weight*depth)

Vertical stresses in soils

• defined in terms of total & effective stress components

• due to self-weight of soil & external loads

𝝈_z=total vertical stress component normal to the horizontal plane of a soil element in the ground at depth

𝝈_x and 𝝈_y = total vertical stress components normal to the vertical planes

Vertical stress (due to self weight) in dry soil

• increases linearly with depth in homogeneous soil deposits

𝝈_z=𝛾_d*z=𝜌_d*g*z

Vertical stress (due to self weight) in saturated soil

• increases linearly with depth in homogeneous soil deposits

𝝈_z=𝛾_sat*z=𝜌_sat*g*z

Pore pressure (hydrostatic - no flow/ seepage)

u=𝛾_w*z=𝜌_w*g*z

u=water pressure

𝛾_w=unit weight of water

𝜌_w=density of water

• increases linearly with depth

Total stress

𝝈

Total stress = Pore water pressure + Effective stress

Pore water pressure

u

= pressure of water filling voids of saturated soil ➞ lifts particles / resists stress

Effective stress

𝝈’

= net stress supported by soil skeleton

effective stress ≠ contact part (is an average)

𝝈’=𝝈-u

• all measurable effects resulting from stress changes in the soil such as compression, distortion and shearing resistance variations are solely due to changes in effective stresses (not total stresses)

Stress transfer within soil mass

Average value of stress over a region

• 2 materials co-exist at each point → solid skeleton + fluid voids

Effective vertical stresses (due to self weight) formula

𝝈’z=𝛾_sat*z-𝛾_w*z=(𝜌_sat-𝜌_w)*g*z

𝛾’=effective unit weight of soil=𝛾_sat-𝛾_w

• increase linearly with depth in homogeneous soil deposits

Capillary rise

h_c is proportional to 1/d

h_c = capillary rise

d = capillary tube diameter

• due to capillary pore pressure (becomes negative above water level)

Variation of degree of saturation in sand column

h₁=C/(e*D₁₀)

e=void ratio

D₁₀=effective size (mm)

C=constant (10-50mm²)

Pore water pressure in capillary zone in sands

u=-h_c*𝛾_w*S_r

𝛾_w = specific weight of water = 9.81 kN/m³

Draw the variation of σ_z , u, and σ’_z with depth for the soil profile shown below. The sand layer within 1 m above the ground water table is fully saturated

Specific weight of water

9.81 kN/m³

Finding y_sat

Find e with y_dry then calculate y_sat

Effective stress in saturated soils defines

• strength

• stiffness

• deformation