Foundation Engineering

Lateral piles, elastic foundation, pile wave propagation & ground improvement

Domain

Explanation

Remarks

Laterally loaded piles
  • Design criteria:
  1. ULS: F.O.S. against soil/pile failure
  2. SLS: tolerable deflection & rotation (main design criterion)
  • Applications, use:
  • Port structures
  • Offshore, earth-retaining, earthquake, tunnels & transmission structures
  • Approaches:
  1. Statical approach: g Hu < g .Pu
  2. Ultimate soil pressure: Kq,Kc,Kp
  3. Brom's theory: in (cohesive 9.cu/ cohesionless Kp) soils for (short, intermediate, long) piles with (free, fixed) heads of (single, group a ) behaviour
  • Lateral piles design:
  1. Loading
  2. Soil bearing capacity & settlement
  3. Pile capacity
  4. Balance of (loading, capacity)
  • Lateral deflections & rotations:
  1. Elastic: Poulos & Davis 1980
  2. Modulus of subgrade: elastic fn.
  • Models dependent on soil modulus, Es
  • r & q calculated from Hu & Mu to be tolerable

Beam on elastic foundation
  • Basis: Winkler model
  • Modeling soil as independent springs with either constant or varying modulus
  • Beams: short (l L<p /4), semi-infinite & long (l L>p ) infinite
  • Modulus of subgrade reaction (Ko): effects of (size, shape, depth)
  • Applicable to:
  • Rigid beam: w constant
  • Flexible beam: w variable - use trigo. rep.
  • NAVFAC 1982: induced loads & deflection by finite difference method
    • Tutorial 1: pile capacity
    • Design as in BS8110, RC pile & reinforcement amount
  • Tutorial 2: d of free head > fixed head
  • d at constant av. modulus < d at variable modulus

    • Wave propagation
    • 1-D wave equation: c2.d 2u/d x2=d 2u/d t2, c=sqrt(E/r )
    • Induced stresses: F=s A=E.A.v/c
    • Discontinuity: ensure compatibility of displacement (left=right) & forces (FI+Frefl=Frefr)
  • Solution: fixed (u=0), free (s =0)
  • U(x,t)=f1(x-ct)+f2(x+ct)
  • Forward + backward propagation
  • Incident wave = reflected wave + refracted wave
    • Wave equation method:
    • r .A.d 2u/d t2-A.E.d 2u/d x2+ks.u+cs.d u/d t=0
    • Soil model for pile soil interaction: EAL Smith 1960 & Randolph and Simons (1986,1990)
  • Solution: analytical difficult, numerical include FDM, FEM & Method of Characteristics
  • Applicability:
    1. Prediction of pile predictability
    2. Driving stresses in piles
    3. BC of piles from set measurements
    4. BC of piles from stress-wave measurements for dynamic pile analysis
    • Assumptions: constant section of homogeneous material + self-weight is ignored
    • Modeling: appropriate assumptions needed before solution
  • Section changes:
    1. Uniform: a =I2/I1=E2/E1=1, all refracted
    2. Narrowing or softening: a <1, reflected compressive strain
    3. Widening or hardening: a >1, reflected tensile strain

    Ground improvement
    • Modify ground for objectives for less movement, higher F.O.S., hasten consolidation & prevent dynamic liquefaction
    • Properties of strength (BC), modulus (Es, ks), compressibility (mv), shrinkage/swelling & permeability (kI)
  • Improvement method:
    1. Mechanical: vibration, compaction & tamping
    2. Hydraulic: wells, drains, drainage paths
    3. Physical & chemical: jet grouting & cementitious , deep cement mixing, lime column & sand compaction piles (SCP)
    4. Confinement: reinforcement, nails & anchors

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