Foundation Engineering

A structured learning path from bearing capacity theory through advanced foundation design. Master shallow foundations, deep foundations, pile systems, retaining walls, and settlement analysis.

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Level 1

Beginner — Bearing Capacity and Shallow Foundations

Start here if you are new to foundation engineering.

Bearing Capacity Theories (Terzaghi, Meyerhof, Hansen)

Bearing capacity is the ability of soil to support foundation loads without shear failure. Terzaghi's bearing capacity equation established the fundamental form: qult = cNc + γDfNq + 0.5γBNγ, where Nc, Nq, and Nγ are bearing capacity factors depending on the soil friction angle φ. Terzaghi's solution assumes general shear failure in a rigid-plastic soil mass, with the failure surface consisting of an active Rankine zone immediately below the footing, a radial shear (Prandtl) zone, and a passive Rankine zone.

Meyerhof's method extended bearing capacity analysis to account for shape, depth, and inclination factors, providing more accurate results for practical conditions. Meyerhof's equation: qult = cNc·sc·dc·ic + qNq·sq·dq·iq + 0.5γBNγ·sγ·dγ·iγ. Hansen further refined the factors, including base inclination and ground slope factors. Vesic's method is preferred for soils with high friction angles. For saturated clays under undrained conditions (φ = 0), Nc = 5.14, and qult = 5.14·su + γDf. Use the Soil Bearing Capacity Calculator to apply these methods to your projects.

Types of Shallow Foundations

Shallow foundations transfer loads to soil near the ground surface, with depth typically less than the footing width. Isolated spread footings are the most common type, supporting individual columns with square, rectangular, or circular plan dimensions. Wall footings (strip footings) support continuous load-bearing walls and are designed as 1 m wide strips. Combined footings support two or more columns and are used when columns are close together or near property lines, where eccentric loading is unavoidable.

Mat (raft) foundations are thick concrete slabs covering the entire building footprint, used when soil bearing capacity is low and individual footings would cover more than 50-60% of the area. Raft foundations distribute structural loads over a large area, reducing bearing pressure and differential settlement. Flat plate mats, thickened under columns, and beam-stiffened mats are common configurations. Basement walls acting as retaining structures combined with mat slabs provide both foundation and below-grade enclosure.

Soil Investigation and Site Exploration

A thorough site investigation is essential for foundation design. The investigation program includes desk study, site reconnaissance, subsurface exploration, laboratory testing, and geotechnical reporting. Boring locations are typically spaced at 15-30 m for buildings, with at least one boring per structure and a minimum of three for large projects. The depth of boring should extend through all unsuitable strata to a depth where the stress increase from the foundation is less than 10% of the existing overburden pressure.

The Standard Penetration Test (SPT) per ASTM D1586 is the most widely used field test, providing N-values correlated to soil strength and density. For cohesive soils, undisturbed tube sampling provides specimens for triaxial and consolidation testing. The Cone Penetration Test (CPT) provides continuous soil profiling and direct measurements of tip resistance and sleeve friction. Laboratory tests include classification (Atterberg limits, grain size), strength (unconfined compression, triaxial), and consolidation tests. Use the Soil Bearing Capacity Calculator with SPT N-values to estimate bearing capacity.

Level 2

Intermediate — Settlement Analysis and Retaining Walls

Build on fundamentals with deformation and earth retention.

Immediate and Consolidation Settlement

Settlement of foundations has two components: immediate (elastic) settlement occurring during construction and consolidation settlement occurring over time. Immediate settlement in sands and overconsolidated clays is estimated using elastic theory: Si = qB(1-μ²)/E·If, where If is an influence factor depending on foundation shape and rigidity. Schmertmann's method using strain influence factors provides more accurate settlement predictions for granular soils, integrating the product of vertical strain and depth.

Consolidation settlement in saturated clays follows Terzaghi's one-dimensional theory. For normally consolidated clays, Sc = Cc·H/(1+e₀)·log(σ'₀+Δσ/σ'₀), where Cc is the compression index, H is the clay layer thickness, e₀ is the initial void ratio, σ'₀ is the initial effective stress, and Δσ is the stress increase. Overconsolidated clays use the swelling index Cs when loading remains below the preconsolidation pressure. Secondary compression (creep) settlement continues after primary consolidation under constant effective stress. Use the Settlement of Soil Calculator to compute settlements.

Earth Pressure Theory and Retaining Wall Design

Retaining walls must resist lateral earth pressures from retained soil and any surcharge loads. Rankine's theory gives active earth pressure coefficient Ka = tan²(45° - φ/2) for level backfill, and passive Kp = tan²(45° + φ/2). Coulomb's theory accounts for wall friction and sloping backfill but is more complex. The lateral earth pressure at any depth z is σh = Ka·γ·z - 2c√Ka for active conditions in cohesive-frictional soils. At-rest pressure coefficient K₀ = 1 - sinφ for normally consolidated soils.

Cantilever retaining walls are the most common type for heights up to 6-8 m, consisting of a vertical stem and a base slab (heel and toe). Stability checks include: overturning about the toe (FS ≥ 2.0), sliding along the base (FS ≥ 1.5), bearing pressure (maximum ≤ allowable, no tension for drained conditions), and global stability. The stem is designed as a cantilever slab for the triangular earth pressure distribution. Drainage is critical — weep holes and granular backfill prevent hydrostatic pressure buildup. Use the Retaining Wall Design Calculator for stability analysis.

Design of Mat/Raft Foundations

Raft foundations are used when individual footings would cover a large proportion of the building area, or when differential settlement must be minimized. The rigid method assumes linear distribution of soil pressure under the raft: q = ΣP/A ± ΣM·x/I. The raft is analyzed as a beam or slab with upward soil pressure acting against downward column loads. Flat plate rafts require punching shear checks at each column and flexural reinforcement design for critical moment sections.

For more accurate analysis of rafts on compressible soils, the Winkler spring model (modulus of subgrade reaction k) represents soil-structure interaction. The subgrade modulus k can be estimated from plate load tests or empirical correlations with SPT N-values and soil type. Finite element analysis using thick plate elements with elastic spring supports provides detailed moment, shear, and settlement distributions. Differential settlement criteria typically limit angular distortion to 1/300 for structural frames and 1/500 for load-bearing walls. Piled rafts combine bearing elements for very high loads on soft soils.

Level 3

Advanced — Deep Foundations and Pile Design

For senior students and practicing engineers.

Pile Foundation Types and Selection

Deep foundations transfer loads through weak surface soils to stronger bearing strata at depth. Piles are classified by material (concrete, steel, timber, composite), installation method (driven, bored, CFA, screw), and load transfer mechanism (end-bearing, friction, or combination). Driven precast concrete piles are cost-effective for large projects with good driving conditions. Bored cast-in-situ piles (drilled shafts) are suitable where vibration or noise must be minimized and where large diameters (up to 3 m) are required.

Continuous Flight Auger (CFA) piles are installed by rotating a hollow-stem auger into the ground, then pumping concrete through the auger as it is withdrawn, with a reinforcement cage inserted immediately afterward. Screw piles (displacement piles) have a steel shaft with helical plates, installed by torque — popular for solar farms and lightweight structures due to immediate load capacity. Micropiles (mini-piles) of 100-300 mm diameter can be installed in restricted access and low headroom conditions, often used for underpinning existing structures.

Pile Load Capacity — Static and Dynamic Methods

The ultimate geotechnical capacity of a pile Qu = Qb + Qs — end bearing plus skin friction. Static analysis for driven piles uses effective stress methods: Qs = Σ(K·σ'v·tanδ)·As·ΔL and Qb = Nq·σ'v·Ab, where K is the lateral earth pressure coefficient, δ is the soil-pile friction angle, and Nq is the bearing capacity factor (typically 25-80 for dense sands). For bored piles in clay, the alpha method (total stress) uses α·su for skin friction, where α ranges from 0.3 to 1.0 depending on su. Beta method (effective stress) uses β·σ'v for skin friction.

Dynamic methods include the driving formula (Hiley, Gates) relating driving resistance to static capacity, and the more accurate Pile Driving Analyzer (PDA) with CAPWAP analysis for wave equation matching. Static load tests per ASTM D1143 remain the most reliable method — the maintained load test applies load in increments to at least 200% of the design load. Pile group efficiency depends on spacing, with typical minimum spacing of 3 pile diameters (center-to-center) and efficiency η = 1 - θ/90 × [(n-1)m + (m-1)n]/(mn) using the Converse-Labarre formula. Negative skin friction from consolidating soil around piles adds downdrag load that must be considered. Use the Pile Foundation Calculator for capacity estimation.

Slope Stability and Ground Improvement

Slope stability analysis evaluates the factor of safety against sliding along potential failure surfaces. The infinite slope method for shallow translational slides in cohesionless soils: FS = (tanφ)/(tanβ). For deeper rotational failures, the Swedish circle method (Fellenius) and Bishop's simplified method divide the sliding mass into vertical slices. Bishop's method is preferred for its accuracy: FS = Σ[c'b + (W - ub)tanφ']/mα / ΣWsinα, where mα = cosα(1 + tanα·tanφ'/FS). Critical failure surfaces are found by searching trial circles to identify the minimum FS.

Ground improvement techniques modify soil properties to improve bearing capacity, reduce settlement, or accelerate consolidation. Vibro-compaction densifies granular soils using depth vibrators. Stone columns provide both reinforcement and drainage in soft cohesive soils. Preloading with vertical drains (PVDs) accelerates consolidation settlement before construction. Soil mixing (deep mixing method) creates soil-cement columns with improved strength and stiffness. Jet grouting erodes and mixes soil with cement grout at high pressure, forming columns or panels of improved ground. Use the Slope Stability Calculator for factor of safety analysis.

Practice Exercises

Exercise 1: Bearing Capacity Calculation

A square footing 2 m × 2 m is founded at 1.5 m depth in sandy soil with γ = 18 kN/m³, c = 0, and φ = 32°. Using Terzaghi's method, calculate the ultimate bearing capacity and the allowable bearing capacity with FS = 3. Verify with the Soil Bearing Capacity Calculator.

Exercise 2: Settlement Analysis

A 3 m × 3 m footing carrying 1500 kN load rests on a clay layer 6 m thick with e₀ = 0.8, Cc = 0.35, and σ'₀ = 80 kPa at mid-depth. The groundwater table is at the foundation base. Calculate the consolidation settlement assuming normally consolidated clay. Use the Settlement of Soil Calculator to verify.

Exercise 3: Retaining Wall Stability

A 5 m high cantilever retaining wall with a 0.5 m thick stem and 3.5 m wide base retains granular backfill with γ = 18 kN/m³ and φ = 34°. The base friction angle is 30°. Check factors of safety against overturning and sliding. Use the Retaining Wall Design Calculator to verify.

Exercise 4: Pile Capacity

A 450 mm diameter bored pile extends 12 m through clay with su = 50 kPa (top 6 m) and su = 80 kPa (bottom 6 m). The pile end bears on stiff clay with Nc = 9. Using the alpha method (α = 0.6 for su = 50 kPa, α = 0.4 for su = 80 kPa), calculate the ultimate compression capacity. Verify with the Pile Foundation Calculator.

References

Bowles, J.E. Foundation Analysis and Design. 5th ed., McGraw-Hill, 1996.
Coduto, D.P. Foundation Design: Principles and Practices. 3rd ed., Pearson, 2016.
Das, B.M. Principles of Foundation Engineering. 8th ed., Cengage Learning, 2016.
Terzaghi, K., Peck, R.B., and Mesri, G. Soil Mechanics in Engineering Practice. 3rd ed., Wiley, 1996.
Tomlinson, M.J. and Woodward, J. Pile Design and Construction Practice. 6th ed., CRC Press, 2014.
EN 1997-1. Eurocode 7: Geotechnical Design. European Committee for Standardization, 2004.
Civil Engineering Handbook — Foundation Engineering chapter.
Engineering Formula Library — Geotechnical formulas.
Engineering Standards Reference — ACI and Eurocode provisions.
Engineering Glossary — Definitions of foundation engineering terms.