Geotechnics and Water Engineering

Sand (Drained) Piles

Drained analysis are driven by the friction angle, and therefore;

• τs,ave = K ⋅ σv′​ ⋅ tanδ

• Qb = σv′ ⋅ Nq

• C = C’ (assumed to be 0)

Driven Piles;

• Ko < K < Kp

• Loose sand k = 1

• Dense (Io=0.8) sand k = 2

Bored Piles;

• ko > K > Ka

• All sands 0.7 < K < 1.0

Clay (Un-Drained) Piles

Undrained analysis are governed by the cohesion / shear strength, Cu, and therefore;

• τs,ave = α⋅cu

• Qb = Cu ⋅ Nc

• C = Cu

0.5 < α < 1.0

• 0.5 = overly consolidated

• 1.0 = Normally consolidated

Groups (Piles)

• In groups the piles are assumed to act as one singular unit and therefore you covert it to a rectangle by timesing the centre-to-centre by the diameter (for a circular pile).

• For piles α = 1 (always).

• As = Surface area (for the shaft this is taken by the depth of the layer e.g. 0 → 5m, 5 → 15m) (base = top surface area, shaft = sides surface area).

Critical State Model

Define the Axes:

• Draw axes q vs p’ and V vs p’.

Construct the V − ln(p′) Plot:

• Draw the Isotropic Normal Compression Line (INCL), straight line with slope −λ. Normal Compression Line Equation V = Vλ ​−λ*ln(p′).

• Draw the unload-reload line (URL). This represents the elastic states. Soil samples move along this line when they are over-consolidated.

• Draw critical state line (CSL). The CSL represents the state where soil shears at constant volume and constant stress. V = Γ−λ*ln(p′).

Construct the q−p′ Plot:

• Draw critical state line (the double line). p’=? starts. q = M ⋅ p′ (this equation isn’t kind of on formula sheet).

• Draw the Cam-Clay Yield Surface. Draw a semi-elliptical curve (the yield locus) that starts at the origin and intersects the p′-axis at the pre-consolidation pressure (pv′​).

The Triaxial Stress Paths:

• For a Drained Test: Draw a path with a slope of Δq/Δp′=3 starting from the initial stress state (Total Stress Path).

• For Un-Drained Test: Draw a path with slope 3 (Total Stress Path).