Glossary

6.3 Calculation of settlement (immediate, primary, and secondary)

5 min readā€¢august 16, 2024

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

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  • 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 (, gravel)
  • manifests as time-dependent deformation in saturated fine-grained soils
    • Results from excess pore water pressure dissipation
    • Leads to a reduction in
    • More pronounced in cohesive soils (, )
  • settlement continues after primary consolidation under constant
    • 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: Si=qāˆ—Bāˆ—(1āˆ’Ī½2)āˆ—If/EsS_i = q * B * (1 - Ī½^2) * I_f / E_s
    • Si: immediate settlement
    • q: applied stress
    • B: foundation width
    • Ī½:
    • If: influence factor
    • Es:
  • Key soil parameters for calculations:
    • Elastic modulus (Es): measure of soil stiffness (higher values indicate stiffer soil)
    • Poisson's ratio (Ī½): 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

  • forms the basis for calculating primary consolidation settlement in saturated fine-grained soils
  • Primary consolidation settlement equation: Sc=Hāˆ—Cc1+e0āˆ—logā”(Ļƒfā€²Ļƒ0ā€²)S_c = H * \frac{C_c}{1 + e_0} * \log(\frac{Ļƒ'_f}{Ļƒ'_0})
    • Sc: consolidation settlement
    • H: layer thickness
    • Cc:
    • e0: initial void ratio
    • Ļƒ'f: final effective stress
    • Ļƒ'0: initial effective stress
  • Key parameters determined from laboratory consolidation tests (oedometer):
    • Compression index (Cc): slope of the virgin compression line in e-log Ļƒ' space
    • Initial void ratio (e0): ratio of void volume to solid volume in soil sample
    • (Ļƒ'p): maximum past effective stress experienced by the soil

Stress Distribution and Soil Behavior

  • Stress distribution methods calculate increase in effective stress (Ī”Ļƒ') 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 (Ļƒ'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, (Cr) used for stress ranges below Ļƒ'p
    • Cr typically 5-10% of Cc, resulting in smaller settlements for overconsolidated soils

Time-Dependent Consolidation Behavior

  • (cv) describes time-dependent consolidation:
    • Used to estimate rate of settlement and
    • 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
  • (Tv) relates time, drainage conditions, and soil properties: Tv=cvāˆ—tHd2T_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: Ss=Hāˆ—CĪ±āˆ—logā”(t2t1)S_s = H * C_Ī± * \log(\frac{t_2}{t_1})
    • Ss: secondary settlement
    • H: layer thickness
    • CĪ±:
    • t2 and t1: time intervals after end of primary consolidation
  • Secondary compression index (CĪ±) 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
  • CĪ±/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 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

Key Terms to Review (28)

Angle of internal friction: The angle of internal friction is a measure of the shear strength of soil, which describes the resistance to sliding or deformation when stress is applied. This angle plays a critical role in understanding how soil behaves under load, influencing calculations related to stability, bearing capacity, and settlement. Higher values indicate better soil strength and stability, while lower values suggest weaker soil that may be more susceptible to failure.
Clay: Clay is a fine-grained natural soil material that becomes plastic when wet and hardens when dried or fired. This unique property allows clay to play a crucial role in various soil classification systems, soil composition, and structure, as well as settlement calculations, shear strength testing, and slope stability analysis.
Coefficient of consolidation: The coefficient of consolidation is a parameter that measures the rate at which soil consolidates under load, specifically the time-dependent decrease in volume due to expulsion of pore water. It is critical for understanding how different types of soil behave under applied loads and directly ties into concepts such as settlement calculations, consolidation theory, and performance of foundations.
Cohesion: Cohesion is the property of soil that describes the attraction between soil particles, which contributes to the soil's strength and stability. This internal binding force is essential in understanding how soil behaves under different conditions, including how it interacts with moisture, external loads, and other forces acting on it.
Compressibility: Compressibility is a measure of how much a material decreases in volume under applied stress. It is crucial for understanding how soils respond to loads, especially in scenarios involving layered soils, settlement calculations, and the design of shallow foundations. The compressibility of soil influences how much it will deform under a given load, which directly affects the stability and performance of structures built on or in the ground.
Compression Index: The compression index is a parameter that quantifies the compressibility of soil when subjected to an increase in effective stress during consolidation. It is crucial for understanding how much a saturated soil will compress under load, which is essential in predicting settlement behavior over time and assessing stability.
Consolidation Time: Consolidation time refers to the duration it takes for soil to undergo the process of consolidation, which is the gradual reduction of volume under applied load due to the expulsion of water from the soil's voids. This process is crucial in understanding settlement, as it directly impacts immediate, primary, and secondary settlement types. A comprehensive grasp of consolidation time helps predict how quickly a soil will stabilize under loads, influencing foundation design and construction timelines.
Degree of consolidation: The degree of consolidation refers to the extent to which soil has undergone consolidation, which is the process of volume reduction due to expulsion of water from the soil pores under applied load. This term is crucial in understanding how much a saturated soil will settle over time when subjected to stress, impacting immediate, primary, and secondary settlement calculations. A higher degree of consolidation indicates that more water has been expelled and the soil has settled significantly.
Dilatancy: Dilatancy is the property of certain materials, especially granular soils, that causes them to increase in volume when subjected to shear stress. This phenomenon occurs when the soil particles rearrange themselves during deformation, leading to an increase in void space. Dilatancy can significantly affect the behavior of soils under loading and influences their settlement characteristics and shear strength, particularly in different drainage conditions and with varying soil types.
Drainage condition: Drainage condition refers to the state of water movement and retention in soil, which greatly influences soil behavior, strength, and settlement characteristics. Understanding drainage conditions is essential in predicting how soil will react under various loading conditions, particularly when calculating settlement due to immediate, primary, and secondary factors. These conditions can be classified as fully drained, partially drained, or undrained, affecting how pore water pressure dissipates over time.
Effective Stress: Effective stress is the stress that contributes to the strength and stability of soil, representing the difference between total stress and pore water pressure within the soil. This concept is crucial in understanding how soil behaves under various conditions, particularly in the context of fluid movement, consolidation, and strength properties of soils.
Elastic modulus: Elastic modulus is a measure of a material's ability to deform elastically when a force is applied. It reflects the relationship between stress (force per unit area) and strain (deformation) in materials, indicating how much a material will stretch or compress under load. This property is crucial in understanding the behavior of soils and foundations when subjected to loads, impacting theories of stress distribution and settlement calculations.
Immediate settlement: Immediate settlement refers to the instantaneous change in vertical position of a foundation when a load is applied, typically occurring within a short time frame after loading. This type of settlement primarily results from the compression of soil under the applied load, particularly in saturated soils where pore water pressure may change. Understanding immediate settlement is crucial for evaluating the performance of foundations, as it directly affects structural integrity and safety.
Oedometer Test: The oedometer test is a laboratory procedure used to assess the consolidation properties of soil by measuring its deformation under a controlled load over time. This test provides crucial insights into how soil behaves under stress, especially in relation to consolidation theory and its implications for settlement analysis and foundation design.
One-dimensional consolidation equation: The one-dimensional consolidation equation describes how a saturated soil layer consolidates over time when subjected to an increase in effective stress. This equation is fundamental in geotechnical engineering for predicting the settlement of foundations and other structures due to loading, and it links the rate of consolidation to soil properties such as permeability and compressibility.
Plasticity Index: The plasticity index is a numerical value that represents the plasticity of a soil, calculated as the difference between the liquid limit and the plastic limit. It helps in understanding how a soil behaves under different moisture conditions, indicating its capacity to deform without cracking. This index is crucial in assessing soil behavior during construction, as it influences settlement characteristics, foundation performance, and the effectiveness of stabilization methods.
Poisson's Ratio: Poisson's ratio is a measure of the elastic behavior of materials, defined as the ratio of the transverse strain to the axial strain when a material is subjected to uniaxial stress. This concept is crucial in understanding how materials deform under load, affecting factors such as settlement calculations and the performance of shallow foundations. It helps predict how much a material will expand or contract in directions perpendicular to the applied load, making it important for engineers assessing structural stability and ground movement.
Preconsolidation pressure: Preconsolidation pressure is the maximum vertical stress that a soil has experienced in the past due to loading before the application of any additional load. This pressure is crucial in understanding how soil will behave under new loads and is used to predict settlement behavior, especially in the context of immediate, primary, and secondary settlement processes, as well as in assessing consolidation settlement of foundations.
Primary consolidation settlement: Primary consolidation settlement is the process by which saturated soil decreases in volume due to the expulsion of pore water from its voids under sustained loading. This phenomenon is critical for understanding how structures interact with the ground over time as the soil gradually consolidates under the applied load, ultimately affecting stability and performance. This settlement occurs over a period of time and is distinct from immediate settlement, which happens right after loading, and secondary consolidation, which involves additional long-term adjustments.
Recompression Index: The recompression index is a measure of the compressibility of soil when it is subjected to unloading and then reloading, indicating how much the soil will compact upon being reloaded after being allowed to expand. This index is crucial for understanding how soil behaves under changes in loading conditions, particularly in predicting settlement behavior after construction. It reflects the soil's ability to regain its original volume and is a key factor in calculating settlements for structures, especially shallow foundations and during primary and secondary consolidation phases.
Sand: Sand is a granular material composed of finely divided rock and mineral particles, typically defined as having a grain size between 0.0625 mm and 2 mm. It plays a crucial role in soil mechanics, affecting various properties like drainage, compaction, and strength of the soil, making it essential in many engineering and geological applications.
Secondary compression: Secondary compression refers to the gradual and long-term deformation of soil that occurs after primary consolidation has taken place. This process is particularly significant in fine-grained soils, such as clays, where additional settlement can continue to occur due to factors like particle rearrangement, changes in pore water pressure, and the dissipation of excess pore pressure over time. Understanding secondary compression is essential for accurate predictions of settlement in various geotechnical applications.
Secondary compression index: The secondary compression index is a parameter that quantifies the magnitude of secondary compression in soil, representing the time-dependent deformation that occurs after primary consolidation due to the gradual rearrangement of soil particles. It is an important factor in understanding long-term settlement behavior in saturated soils, especially those with clayey characteristics, as it helps in predicting how much additional settlement may occur over time.
Silt: Silt is a fine-grained soil particle that ranges in size from 0.002 to 0.05 millimeters, falling between sand and clay on the soil texture scale. This particle size plays a significant role in soil behavior, affecting drainage, nutrient retention, and the engineering properties of the soil.
Swell Test: A swell test is a laboratory procedure used to measure the volume change of a soil sample when it is subjected to changes in moisture content. This test helps determine the swell potential of expansive soils, which can significantly impact foundation design and settlement calculations. By understanding how soil swells, engineers can predict immediate, primary, and secondary settlements that may occur once a structure is built.
Terzaghi's Theory: Terzaghi's Theory is a fundamental concept in geotechnical engineering that focuses on the behavior of saturated soils under loading conditions. It primarily deals with the analysis of settlement and consolidation of soil layers, highlighting how different types of settlements occur when structures are built on or within the ground. The theory differentiates between immediate settlement, primary consolidation, and secondary consolidation, providing essential insights into the time-dependent behavior of soil and its deformation characteristics under applied loads.
Time factor: The time factor is a measure of the rate at which consolidation and settlement occur in soils over time, specifically related to the change in effective stress and volume reduction. Understanding the time factor is crucial for predicting how quickly a structure may settle after loading, helping engineers assess when it is safe for construction or use. It plays a significant role in differentiating between immediate settlement, primary consolidation, and secondary consolidation.
Void Ratio: The void ratio is a fundamental soil property defined as the ratio of the volume of voids (spaces between soil particles) to the volume of solid particles in a soil sample. This term is crucial for understanding soil behavior, including how water interacts with soil, its compaction characteristics, and its strength under different conditions.
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