Calculating settlement is crucial for predicting how structures will behave on different soils. We'll look at three types: immediate, primary, and secondary settlement. Each type occurs in different soil conditions and timeframes, affecting building stability.

Understanding these settlement types helps engineers design safer, more stable foundations. We'll explore how to calculate each type, considering factors like soil properties, loading conditions, and time. This knowledge is key for creating structures that stand strong for years to come.

Settlement Types

Immediate, Primary, and Secondary Settlement Characteristics

• Immediate settlement occurs rapidly due to elastic deformation of soil without changes in water content
  • Typically happens in coarse-grained soils or unsaturated fine-grained soils
  • More significant in granular soils (sand, gravel)
• Primary consolidation settlement manifests as time-dependent deformation in saturated fine-grained soils
  • Results from excess pore water pressure dissipation
  • Leads to a reduction in void ratio
  • More pronounced in cohesive soils (clay, silt)
• Secondary compression settlement continues after primary consolidation under constant effective stress
  • Also known as creep
  • Occurs over extended periods, potentially lasting decades or centuries
  • Particularly significant in highly organic soils (peat) and some high-plasticity clays

Factors Influencing Settlement Types

• Relative magnitude and time scale of each settlement type vary based on:
  • Soil type (granular vs cohesive)
  • Loading conditions (magnitude, distribution)
  • Drainage characteristics (permeability, layer thickness)
• Total settlement of a structure combines immediate, primary consolidation, and secondary compression settlements
• Soil mineralogy affects settlement behavior, especially in clay soils
• Stress history influences settlement magnitude, particularly for overconsolidated soils
• Temperature changes can impact long-term settlement, especially in fine-grained soils

Immediate Settlement Calculation

Elastic Theory and Key Parameters

• Immediate settlement calculation employs elastic theory
  • Assumes linear stress-strain behavior
  • Assumes constant soil properties
• General equation for immediate settlement: $S_i = q * B * (1 - ν^2) I_f / E_s$
  • Si: immediate settlement
  • q: applied stress
  • B: foundation width
  • ν: Poisson's ratio
  • If: influence factor
  • Es: elastic modulus
• Key soil parameters for calculations:
  • Elastic modulus (Es): measure of soil stiffness (higher values indicate stiffer soil)
  • Poisson's ratio (ν): ratio of lateral to axial strain (typically 0.3-0.4 for most soils)
  • Obtained from laboratory tests (triaxial, plate load) or empirical correlations

Influence Factors and Complex Conditions

• Influence factors (If) account for:
  • Foundation shape (circular, rectangular, square)
  • Foundation rigidity (flexible vs rigid)
  • Embedment depth (surface vs embedded foundations)
• Determined using charts or equations based on elastic theory (Steinbrenner, Fox)
• Principle of superposition applied for complex loading conditions or layered soil profiles
  • Allows calculation of settlement for multiple loads or soil layers by summing individual contributions
• Corrections for foundation depth and three-dimensional effects improve accuracy
  • Embedment factor reduces settlement for deep foundations
  • Shape factor accounts for three-dimensional stress distribution

Application in Foundation Design

• Immediate settlement calculations often used with allowable settlement criteria
  • Typical allowable settlements range from 25-50 mm for most structures
  • More stringent criteria for sensitive structures (0.1-1% of foundation width)
• Differential settlement between adjacent footings or across large foundations critical for structural integrity
  • Generally limited to 1/500 to 1/1000 of the distance between settlement points
• Iterative process may be necessary to optimize foundation dimensions and meet settlement criteria

Primary Consolidation Settlement

Terzaghi's One-Dimensional Consolidation Theory

• Terzaghi's theory forms the basis for calculating primary consolidation settlement in saturated fine-grained soils
• Primary consolidation settlement equation: $S_c = H * \frac{C_c}{1 + e_0} * \log(\frac{σ'_f}{σ'_0})$
  • Sc: consolidation settlement
  • H: layer thickness
  • Cc: compression index
  • e0: initial void ratio
  • σ'f: final effective stress
  • σ'0: initial effective stress
• Key parameters determined from laboratory consolidation tests (oedometer):
  • Compression index (Cc): slope of the virgin compression line in e-log σ' space
  • Initial void ratio (e0): ratio of void volume to solid volume in soil sample
  • Preconsolidation pressure (σ'p): maximum past effective stress experienced by the soil

Stress Distribution and Soil Behavior

• Stress distribution methods calculate increase in effective stress (Δσ') at various depths:
  • 2:1 method: simple approximation for stress distribution beneath foundations
  • Boussinesq's theory: more accurate stress distribution based on elastic half-space
• Preconsolidation pressure (σ'p) distinguishes between:
  • Normally consolidated soil: current effective stress equals maximum past stress
  • Overconsolidated soil: current effective stress less than maximum past stress
• For overconsolidated soils, recompression index (Cr) used for stress ranges below σ'p
  • Cr typically 5-10% of Cc, resulting in smaller settlements for overconsolidated soils

Time-Dependent Consolidation Behavior

• Coefficient of consolidation (cv) describes time-dependent consolidation:
  • Used to estimate rate of settlement and degree of consolidation
  • Determined from laboratory consolidation tests using log-time or square-root-time methods
• Degree of consolidation (U) represents percentage of total primary consolidation completed at a given time
  • U = 0% at start of loading, U = 100% at end of primary consolidation
• Time factor (Tv) relates time, drainage conditions, and soil properties: $T_v = \frac{c_v t}{H_d^2}$
  • t: time since load application
  • Hd: drainage path length (half the layer thickness for double drainage, full thickness for single drainage)

Secondary Compression Settlement

Calculation and Key Parameters

• Secondary compression settlement equation: $S_s = H * C_α * \log(\frac{t_2}{t_1})$
  • Ss: secondary settlement
  • H: layer thickness
  • Cα: secondary compression index
  • t2 and t1: time intervals after end of primary consolidation
• Secondary compression index (Cα) determined from:
  • Slope of the e-log t curve in laboratory consolidation tests after primary consolidation
  • Typically ranges from 0.005 to 0.02 for inorganic clays, up to 0.05 for organic clays
• Cα/Cc ratio (secondary compression index to compression index) estimates long-term creep potential
  • Typical values: 0.01-0.07 for inorganic soils, 0.05-0.10 for organic soils

Factors Influencing Secondary Compression

• Soil mineralogy affects secondary compression behavior
  • Montmorillonite clays exhibit higher secondary compression than kaolinite clays
• Stress history impacts magnitude of secondary compression
  • Normally consolidated soils generally show higher secondary compression than overconsolidated soils
• Temperature changes can accelerate or decelerate secondary compression rates
  • Higher temperatures typically increase secondary compression rates
• Organic content significantly influences secondary compression
  • Highly organic soils (peat, muck) can experience large secondary settlements

Mitigation Strategies and Long-Term Considerations

• Preloading: applying temporary surcharge load to accelerate primary and secondary settlement
  • Reduces post-construction settlement by pre-compressing soil
• Use of lightweight fill materials (expanded polystyrene, lightweight aggregate) reduces overall settlement
• Deep soil improvement techniques:
  • Stone columns or deep mixing methods to reduce compressibility of soft soils
  • Accelerates consolidation and reduces secondary compression potential
• Long-term performance assessment crucial for structures on compressible soils
  • Secondary compression can continue for decades or centuries
  • Monitoring programs may be necessary to track long-term settlement behavior
• Design considerations for secondary compression:
  • Adjustable connections in structures to accommodate differential settlement
  • Planning for future releveling or jacking of structures in highly compressible soils