Foundation Engineering: Design of Shallow and Deep Foundations
The foundation is the interface between a structure and the ground. It must transfer loads from the superstructure to the soil or rock without causing excessive settlement or bearing capacity failure. Foundation engineering is the discipline that designs this critical interface.
Foundation failures are among the most expensive and difficult failures to repair. The Leaning Tower of Pisa required decades of geotechnical work to stabilize its tilt. The Millennium Tower in San Francisco has sunk 450 mm and tilted 15 cm due to foundation settlement in soft bay mud. Getting foundations right the first time is non-negotiable.
Shallow Foundations
Shallow foundations spread loads near the ground surface. They are used where competent bearing soil exists within a few meters of the surface.
Spread Footings
Spread footings support individual columns. A square footing under a column that carries 2,000 kN on soil with allowable bearing capacity of 200 kN/m² requires a minimum area of 10 m², or a 3.2 m × 3.2 m square. The footing thickness is governed by punching shear and flexural reinforcement requirements.
The contact pressure under a footing is not uniform. It is highest at the edges for rigid footings on cohesive soil and higher at the center for flexible footings on granular soil. Most footings are designed assuming uniform pressure for simplicity, with sufficient reinforcement to handle the actual distribution.
Combined Footings and Mat Foundations
Combined footings support two or more columns on a single footing. They are used when columns are too close for individual footings or when property lines prevent centering. The footing shape is proportioned to keep the resultant load within the footing area to minimize differential settlement.
Mat foundations (raft foundations) are continuous slabs that support the entire structure. They distribute heavy column loads over a large area, reducing contact pressure. Masts are used when the allowable bearing capacity is low, when column loads are high, or when differential settlement must be minimized. A mat foundation for a 20-story building might be 1.5 to 3 meters thick with reinforcement of 100 to 200 kg/m³.
Bearing Capacity
The ultimate bearing capacity is the maximum pressure the soil can sustain before shear failure. Terzaghi’s bearing capacity equation is the classic formulation:
qu = cNc + γDfNq + 0.5γBNγ
where c is soil cohesion, γ is soil unit weight, Df is foundation depth, B is foundation width, and Nc, Nq, Nγ are bearing capacity factors that depend on the soil friction angle. For a cohesionless soil like sand with φ = 35°, the Nq factor is approximately 33 and Nγ is approximately 37.
The allowable bearing capacity is the ultimate bearing capacity divided by a factor of safety, typically 2.5 to 3.0. Alternatively, allowable bearing capacity may be governed by settlement — many foundations are designed to a bearing pressure that limits settlement to acceptable values.
Settlement Analysis
Settlement is the vertical movement of the foundation under load. Excessive total settlement can damage utilities and building entrances. Differential settlement — uneven movement between columns — is more damaging because it induces structural stresses.
Immediate Settlement
Immediate settlement occurs as the soil deforms elastically under load without volume change. Sands and gravels experience immediate settlement almost entirely. The settlement is estimated using elastic theory: Si = qB(1-μ²)/Es, where q is contact pressure, B is footing width, μ is Poisson’s ratio, and Es is soil modulus.
Consolidation Settlement
Consolidation settlement occurs in saturated clays as water is expelled from the soil pores under the increased load. This settlement develops over time — months to decades depending on the clay layer thickness and drainage conditions.
Consolidation settlement is calculated from the oedometer test results. The compression index Cc determines the magnitude: Sc = CcH/(1+e0) × log((σ'0+Δσ)/σ'0), where H is clay layer thickness, e0 is initial void ratio, σ'0 is initial effective stress, and Δσ is stress increase.
Allowable Settlement
Building codes and structural design guides specify allowable settlements. For isolated footings on sand, 25 mm total settlement is typically acceptable. For mat foundations on clay, 50 to 75 mm may be acceptable. Differential settlement between adjacent columns is typically limited to 10 to 20 mm.
Deep Foundations
When shallow soils cannot safely support loads, deep foundations transfer loads to deeper competent strata.
Pile Foundations
Piles are slender structural elements driven or drilled into the ground. They transfer loads through end bearing on a hard layer, skin friction along the pile shaft, or a combination of both.
Precast concrete piles, typically square sections of 250 to 500 mm, are driven using pile hammers. The pile driving analyzer measures force and acceleration during driving to estimate static capacity and driving stresses. The Wave Equation analysis (WEAP) models pile driving to optimize hammer selection and prevent damage.
Steel H-piles and pipe piles are driven through dense soils and obstructions that concrete piles cannot penetrate. Steel piles are more expensive per unit of load capacity but offer advantages in installation speed and ability to handle obstructions.
The capacity of a pile is the sum of end bearing and skin friction. Static load tests — applying test loads up to 200 percent of the design load — are the most reliable method for verifying capacity. When load tests are not performed, capacity is estimated using static analysis methods such as the Meyerhof method for sands or the Alpha method for clays and verified through Soil Mechanics Guide principles.
Pile Groups
Piles are typically installed in groups connected by a pile cap. The group efficiency considers the interaction between closely spaced piles. For driven piles in sand, the group capacity may be greater than the sum of individual capacities because the soil is densified by driving. For drilled piles in clay, the group capacity is typically 0.7 to 0.9 times the sum of individual capacities due to stress overlap.
Pile spacing of 3 pile diameters center-to-center is common. Closer spacing reduces group efficiency. Wider spacing requires larger pile caps.
Drilled Shafts (Caissons)
Drilled shafts are deep foundations constructed by excavating a hole and filling it with concrete. They are 0.6 to 3 meters in diameter and can reach depths of 50 meters or more. Drilled shafts are preferred in urban areas where vibration from pile driving would damage adjacent structures.
The shaft capacity is determined from side shear along the concrete-soil interface and end bearing at the base. Drilled shafts can be belled at the base to increase end bearing area in cohesive soils.
Ground Improvement
When existing soil conditions are inadequate, ground improvement can make them suitable. Methods include preloading (surcharging the site to cause consolidation before construction), stone columns (vibratory installation of crushed stone columns that reinforce soft soil), soil mixing (mixing cement or lime with in-situ soil to improve strength), and dynamic compaction (dropping heavy weights to densify granular soils).
Lateral Earth Pressures and Retaining Walls
Foundation engineering also encompasses lateral earth pressure theory needed for retaining wall and basement wall design. The lateral pressure exerted by soil on a wall depends on the wall movement. At-rest pressure occurs when the wall does not move. Active pressure develops when the wall moves away from the soil. Passive pressure develops when the wall is pushed into the soil.
The Rankine theory of lateral earth pressures provides the simplest and most widely used approach. The active earth pressure coefficient Ka = (1 - sinφ) / (1 + sinφ) for a cohesionless soil with friction angle φ. For φ = 30°, Ka = 0.33. The passive coefficient Kp = (1 + sinφ) / (1 - sinφ) = 3.0. Passive pressure is typically three to nine times larger than active pressure for the same soil.
Cantilever retaining walls use the weight of the soil on the heel to resist overturning. The wall must be checked for sliding, overturning, bearing capacity, and structural capacity of the stem. Drainage behind retaining walls is essential — hydrostatic pressure behind an undrained wall can exceed the earth pressure and cause failure.
Frequently Asked Questions
What is the difference between a shallow and deep foundation? Shallow foundations spread loads near the ground surface and are used when competent bearing soil is within 3 to 5 meters of the surface. Deep foundations transfer loads to deeper strata through piles or caissons.
How are foundations protected against frost heave? Foundations must extend below the frost line — the maximum depth of soil freezing. Frost depth ranges from 0 in warm climates to over 2 meters in cold regions. Insulated foundations can reduce required depth.
Can existing foundations be strengthened? Yes. Methods include underpinning (extending foundations to deeper bearing strata), jet grouting (creating load-bearing columns in the soil), and foundation jacking (restoring settled structures to level).
What causes foundation settlement after construction? Common causes include consolidation of underlying compressible soils, rising or falling groundwater tables, tree root activity affecting soil moisture, vibraiton from nearby construction, and leaking water pipes that soften supporting soils.
Soil Mechanics Guide — Geotechnical Engineering — Structural Analysis Basics