Estimating Foundation Settlement in Clay Soils Using Empirical Methods

This article presents an in-depth guide to estimating settlement in cohesive clay soils using empirical formulas. It explores how clays respond to loading, classifies types of settlement, introduces key empirical methods, and walks through worked examples.

Designing safe and durable structures requires more than just structural calculations; it demands a thorough understanding of how the underlying soil will behave under load. One of the most critical aspects of this interaction is settlement—an inevitable process that occurs when soil beneath a foundation compresses. In clay soils, this phenomenon is particularly pronounced and can lead to severe consequences if not properly estimated. Excessive settlement may cause cracking, differential movement, tilting, and even structural failure. Thus, assessing potential settlement during the design stage is an indispensable aspect of geotechnical engineering.

Clay soils present unique challenges. Unlike granular soils such as sand and gravel, clays exhibit complex behavior driven by their high-water content, fine particle size, and low permeability. These characteristics lead to slow consolidation and time-dependent settlement that can continue long after the structure is completed. Because of this, accurate prediction of settlement is not straightforward. Engineers often turn to empirical methods—simplified but reliable tools developed through extensive observation and data correlation. Though not as precise as numerical models, empirical approaches provide practical estimates suitable for design purposes, particularly where field tests are limited or budgets are constrained.

This article presents an in-depth guide to estimating settlement in cohesive clay soils using empirical formulas. It explores how clays respond to loading, classifies types of settlement, introduces key empirical methods, and walks through worked examples. Assumptions, common errors, and practical advice are also discussed. By the end of this article, you will understand how to evaluate settlement using simple but effective tools, ensuring safer foundation designs in clay-dominated environments.

Behavior of Clay Soils Under Load

Clay is composed of fine-grained particles, typically smaller than 0.002 mm, which retain large amounts of water. Due to this, clays have high plasticity and low permeability. These properties affect how the soil reacts when loaded. Unlike sandy soils that settle rapidly, clays deform slowly because pore water cannot escape easily. This slow drainage leads to a prolonged consolidation process, making clay settlements time-dependent and difficult to predict.

When a load is applied to clay, three distinct settlement stages may occur:

• Immediate settlement arises from elastic deformation of the soil matrix and pore fluid. It occurs almost instantly after loading.
• Primary consolidation is the main phase in clay, caused by the dissipation of excess pore water pressure. As the water drains from pores, the soil particles rearrange, leading to volume reduction.
• Secondary settlement or creep occurs after consolidation. It results from long-term particle realignment and plastic deformation within the soil matrix.

Several factors influence these settlement phases:

• Water content and void ratio govern compressibility.
• Clay thickness, overburden pressure, and plasticity index affect time rate and magnitude of settlement.
• Drainage conditions and soil layering modify the settlement profile.

Understanding these behaviors allows engineers to select appropriate prediction methods. The following sections explore empirical approaches that simplify these complex interactions.

Categories of Settlement in Clay Soils

Engineers categorize settlement into three main types, each governed by distinct mechanisms and time scales:

Immediate Settlement

Immediate settlement is elastic and occurs right after load application. Although more significant in sandy or granular soils, it can be observed in stiff, over consolidated clays as well. It is usually calculated using elastic theory, considering shear modulus and applied pressure.

Primary Consolidation Settlement

This is the dominant settlement mechanism in saturated clays. It results from the gradual dissipation of excess pore pressure induced by loading. The process can span months or even years, depending on the clay’s permeability, thickness, and drainage path.

Secondary Settlement (Creep)

This long-term settlement arises after primary consolidation ends. Creep is caused by molecular-level rearrangement in clay particles. It is especially prominent in organic clays, peats, or very soft marine deposits and can continue indefinitely at a decreasing rate.

Among these, primary consolidation is usually the most critical for foundation design in clay soils. The empirical methods discussed next focus on estimating this component.

Overview of Empirical Methods for Estimating Settlement

Empirical methods simplify complex geotechnical behaviors by correlating observed field performance with basic soil properties. These approaches emerged from extensive case histories and laboratory experiments. While they may not capture every nuance of soil behavior, they provide reliable settlement estimates when detailed numerical modeling or field testing is not feasible.

Commonly used empirical methods for settlement in clay include:

• Skempton and Bjerrum Method – incorporates correction factors for field behavior.
• Modified Terzaghi Method – adapts classical consolidation theory for both normal and over consolidated clays.
• Burland and Burbidge Correlation – empirical charts based on field measurements.
• AASHTO Empirical Formula – used mainly in highway and transportation projects.

Each method has different requirements for input data, such as compression index, void ratio, or pre-consolidation pressure. Their application depends on site conditions, data availability, and the type of clay deposit encountered.

Skempton and Bjerrum Method

This method was proposed to improve classical Terzaghi-based predictions by introducing a correction factor (μ) to account for field variability. The formula adjusts lab-based results to reflect field compressibility, sample disturbance, and stratification effects. It is particularly useful for both normally consolidated and over consolidated clays.

The settlement is given by:

S = \mu \cdot \frac{H}{1 + e_0} \cdot C_c \cdot \log_{10} \left( \frac{\sigma_0' + \Delta \sigma}{\sigma_0'} \right)

Where:

• S = settlement (m)
• μ = correction factor (0.4–1.0)
• H = thickness of compressible clay layer (m)
• e₀ = initial void ratio
• C_c = compression index
• σ₀ = initial effective stress (kPa)
• Δσ = increase in stress due to foundation load (kPa)

This method is advantageous when sample disturbance may have reduced lab-measured compressibility. It better reflects in-situ conditions, especially in stratified or layered clays.

Modified Terzaghi Method

Terzaghi’s classical theory of consolidation is still widely used. It is based on one-dimensional consolidation and assumes full saturation, vertical drainage, and uniform loading.

The formula for normally consolidated clay is:

S = \frac{H}{1 + e_0} \cdot C_c \cdot \log_{10} \left( \frac{\sigma_0' + \Delta \sigma}{\sigma_0'} \right)

For over consolidated clays, the formula is adapted as:

S = \frac{H}{1 + e_0} \cdot \left[ C_r \cdot \log_{10} \left( \frac{\sigma_p'}{\sigma_0'} \right) + C_c \cdot \log_{10} \left( \frac{\sigma_0' + \Delta \sigma}{\sigma_p'} \right) \right]

Where:

• σ_p= preconsolidation pressure
• C_r = recompression index

This method is more sensitive to soil stress history and requires accurate lab data from oedometer tests. If the stress path is misunderstood or the sample is disturbed, results may be misleading. Still, it offers a solid foundation for estimating consolidation settlement.

Worked Example: Skempton and Bjerrum Method

Problem

A soft clay deposit is 8 m thick. It has an initial void ratio e₀=1.2, a compression index C_c=0.3 and is subjected to a stress increase Δσ=80 kPa. The existing effective stress is σ₀′=100 kPa. Use a correction factor μ=0.7

Solution

S = 0.7 \cdot \frac{8}{1 + 1.2} \cdot 0.3 \cdot \log_{10} \left( \frac{100 + 80}{100} \right)

S = 0.7 \cdot \frac{8}{2.2} \cdot 0.3 \cdot \log_{10}(1.8)

S = 0.7 \cdot 3.636 \cdot 0.3 \cdot 0.2553 =195mm

Settlement ≈ 195 mm

Worked Example: Modified Terzaghi Method

Problem

An over consolidated clay layer is 6 m thick. It has e₀=0.9, pre-consolidation pressure σp′= 180 kPa, initial effective stress σ0′=120 kPa, and a stress increase Δσ= 60 kPa. Use C_r=0.05, C_c= 0.25.

Solution

S = \frac{6}{1 + 0.9} \cdot \left[ 0.05 \cdot \log_{10} \left( \frac{180}{120} \right) + 0.25 \cdot \log_{10} \left( \frac{180}{180} \right) \right]

S = \frac{6}{1.9} \cdot [0.05 \cdot 0.1761 + 0]

S \approx 0.0278 \text{ m} = 27.8 \text{ mm}

Settlement ≈ 27.8 mm

Key Assumptions and Practical Considerations

Empirical methods operate under simplified assumptions:

• Soil layers are horizontal and homogeneous.
• Load is uniformly distributed.
• Drainage conditions are ideal.
• Soil compressibility parameters are constant.

In practice, these assumptions rarely hold. Soils are often layered, anisotropic, and affected by seasonal moisture variations. Engineers should:

• Use correction factors wisely.
• Rely on site-specific investigations.
• Cross-check empirical results with field measurements when available.

Conclusion: Engineering Judgment Still Matters

Settlement in clay soils is a gradual but potentially destructive process. Without proper anticipation, it can undermine the integrity of structures long after construction. Empirical methods offer a practical means of estimating settlement when data is limited or when budget constraints make sophisticated modeling unfeasible.

Each method—whether Skempton and Bjerrum or Terzaghi-based—has specific use cases, strengths, and limitations. Use them carefully, validate with real-world data, and remain conservative in your assumptions. Most importantly, continue monitoring after construction to ensure actual performance aligns with predictions.

Also See: Settlement of Bored Pile Foundations | Worked Examples

Sources & Citations

• Skempton, A. W., & Bjerrum, L. (1957). A Contribution to the Settlement Analysis of Foundations on Clay.
• Terzaghi, K., Peck, R. B., & Mesri, G. (1996). Soil Mechanics in Engineering Practice.
• Das, B. M. (2010). Principles of Foundation Engineering.
• Craig, R. F. (2004). Soil Mechanics.
• Eurocode 7: Geotechnical Design – Part 1: General Rules.