Foundation Design Framework and Shallow Foundations

Introduction and context

A foundation transfers structural actions to the ground while maintaining adequate safety, acceptable settlement, and serviceable performance. Foundation design is therefore not simply a calculation of bearing capacity. It is a decision process that connects structural loads, soil and groundwater conditions, construction constraints, durability requirements, and uncertainty in the ground model.

A shallow foundation is one whose depth is small relative to its width and whose load is transferred primarily through the soil immediately beneath and around its base. Typical forms are isolated pad foundations, strip foundations, combined footings, and rafts (mats). The choice among them depends on column arrangement, load magnitude, allowable settlement, property boundaries, soil variability, groundwater, and construction economics.

The modern design framework uses two complementary limit states:

• Ultimate limit state (ULS): prevention of collapse or a major failure mechanism such as bearing-capacity failure, sliding, overturning, or structural failure of the footing.
• Serviceability limit state (SLS): control of total and differential settlement, rotation, cracking, vibration, and other conditions that impair use or durability.

A foundation may satisfy ULS yet be unacceptable because settlement damages finishes, services, frames, or adjacent structures. Conversely, a foundation designed only for small settlement may have inadequate resistance to a rare but severe load combination.

Learning objectives

By the end of this chapter, a student should be able to:

1. assemble design actions and ground data into a rational foundation model;
2. distinguish allowable-stress design from partial-factor or load-and-resistance-factor design;
3. calculate bearing capacity for common drained and undrained cases;
4. evaluate eccentricity, effective dimensions, sliding, overturning, and settlement;
5. select and proportion isolated, strip, combined, and raft foundations;
6. communicate assumptions, uncertainties, construction requirements, and limitations professionally.

1. From structural actions to a foundation model

1.1 Ground investigation and design information

A design brief should identify structural geometry and actions, including permanent load, imposed load, wind, seismic action, equipment loads, accidental actions, and construction-stage loads. The geotechnical model should describe soil or rock layers, unit weight, strength parameters, compressibility, groundwater, seasonal changes, fill, cavities, contamination, and nearby foundations or retaining structures.

Important parameters include effective-stress friction angle φ', effective cohesion c', undrained shear strength s_u, unit weight γ, constrained or oedometric modulus, elastic modulus E_s, Poisson’s ratio ν, and permeability. Values must be selected as representative design parameters, not copied uncritically from a single test. Spatial variability and the consequences of failure influence the selection of characteristic and design values.

The investigation should extend below the anticipated influence zone of the footing. It should also identify weak seams, loose saturated sand, expansive soil, collapsible soil, uncontrolled fill, and potential scour or frost effects. Groundwater observations require time and seasonal interpretation; a single measured water level is not necessarily a design maximum.

1.2 Actions, combinations, and contact pressure

Let N be the vertical design action, H the horizontal action, and M the moment at foundation level. The foundation self-weight and soil overburden above the base should be included consistently. For a rectangular footing of width B and length L, the gross base area is

The average gross contact pressure is

where N is in kN and A is in m², giving q in kPa. Net pressure is often defined as the pressure increase relative to the removed overburden; however, gross and net conventions must not be mixed in one calculation.

For a load acting with moment about the centroid, the eccentricities are

where e_B and e_L are eccentricities in the corresponding directions. For one-way eccentricity across width B, the linear pressure distribution is

These expressions assume a rigid footing and a linearly varying contact pressure. If e ≤ B/6, the entire base remains in compression. If e > B/6, the computed q_min is tensile, which soil generally cannot sustain; a compression-only, effective-area analysis is then required. The no-tension criterion in two directions is commonly expressed as e_B ≤ B/6 and e_L ≤ L/6, although the exact pressure distribution depends on footing rigidity and soil response.

1.3 Allowable-stress and factored-resistance approaches

In allowable-stress design, service-level actions are compared with an allowable soil pressure:

The allowable pressure is commonly obtained by dividing a nominal or ultimate resistance by a global factor of safety and then checking settlement separately. This approach is simple but can obscure the different uncertainties associated with loads, soil strength, and failure consequences.

In limit-state design, factored actions are compared with factored resistance:

where E_d is the design effect of actions and R_d is the design resistance. Partial factors may be applied to actions, material properties, or resistance, depending on the adopted code. Load-and-resistance-factor design has the same underlying logic. A designer must use one coherent code format and avoid combining an allowable pressure with already factored loads.

2. Bearing capacity

Bearing-capacity failure occurs when soil beneath or adjacent to a footing develops a continuous shear mechanism. Three broad failure modes are recognized:

• General shear: a clear failure surface and substantial ground heave, usually in dense sand or stiff clay.
• Local shear: progressive failure with limited heave, often in medium-dense or firm soils.
• Punching shear: the footing penetrates relatively compressible soil with little surface heave.

The familiar bearing-capacity equation for a rectangular footing under vertical, centered loading is

Here q_ult is ultimate gross bearing capacity; c' is effective cohesion; q = γ D_f is surcharge at base level; D_f is embedment depth; B is footing width; γ is soil unit weight; N_c, N_q, and N_γ are bearing-capacity factors; and s, d, and i are shape, depth, and load-inclination factors. The equation assumes a suitable strength model, a defined failure mechanism, and consistency between gross or net quantities. Different textbooks and standards use different expressions for N_γ and correction factors; the adopted standard must therefore be stated.

For the classical general-shear, effective-stress solution,

The expression for N_γ is code-dependent; one commonly used approximation is

It should not be substituted automatically when a governing code specifies another formulation.

For undrained analysis of saturated clay under short-term loading, φ_u = 0 and c_u = s_u. A simplified rectangular-footing expression is

with N_c commonly taken as approximately 5.14 for a strip footing in the classical solution. The undrained approach is appropriate only when the loading is rapid relative to drainage and the soil response is represented by total-stress strength.

Effective dimensions for eccentric loading

A practical method for eccentric loading uses an effective area. For a rectangular footing,

The bearing-capacity equation is then evaluated using B' and L' and the pressure N/A'. This method is conservative and convenient, but it is not a complete description of a highly flexible footing or a load close to an edge. If either effective dimension is non-positive, the proposed footing arrangement is unacceptable without redesign.

Worked example 1: preliminary bearing-capacity check

An isolated square footing is 2.0 m × 2.0 m at a depth of 1.0 m in drained soil with γ = 18 kN/m³, c' = 10 kPa, and φ' = 30°. Assume vertical centered loading, general shear, no correction factors, and use N_c = 30.1, N_q = 18.4, and N_γ = 15.7.

The surcharge is q = γD_f = 18 kPa. Thus,

This is a nominal gross ultimate value under the stated assumptions. With a global factor of safety of 3, the corresponding preliminary allowable gross pressure is approximately 305 kPa, subject to the settlement check. If the actual design uses partial factors, this allowable-stress calculation must not be combined with factored actions.

3. Settlement and serviceability

Settlement has immediate, consolidation, and secondary components. Immediate settlement is associated with elastic distortion and occurs during or soon after loading. Consolidation settlement results from drainage and volume reduction in saturated compressible soil. Secondary compression continues after primary consolidation, particularly in organic soils and some clays.

A simplified elastic estimate for a flexible loaded area can be written as

where s_i is immediate settlement, q is net applied pressure, B is a characteristic width, ν is Poisson’s ratio, E_s is soil elastic modulus, and I_s is an influence factor. The equation is an approximation and requires a compatible modulus, load geometry, and influence factor.

For one-dimensional consolidation, the settlement of a normally consolidated layer may be estimated by

where C_c is compression index, H is layer thickness, e₀ is initial void ratio, σ'₀ is initial effective vertical stress, and Δσ' is the stress increase at the representative depth. For an overconsolidated soil, recompression and virgin-compression portions must be treated separately using the preconsolidation stress. Settlement calculations should account for stress distribution with depth, groundwater changes, construction sequence, and interaction among nearby footings.

Design checks include total settlement, differential settlement, angular distortion, tilt, and time rate. Differential settlement is often more damaging than uniform settlement. Numerical limits are project- and code-specific; they should not be presented as universal soil constants.

4. Sliding, overturning, and uplift

For a foundation subjected to horizontal action, sliding resistance may include base friction, passive resistance, and, where justified, mechanical shear keys. A simplified drained friction check is

where μ is the base friction coefficient, V is effective vertical force, P_p is permitted passive resistance, c_a is adhesion, and A_b is base area. Passive resistance and adhesion should not be counted casually: excavation disturbance, groundwater, poor contact, and future landscaping may make them unreliable. A factor of safety or partial-factor requirement is applied according to the design code.

Overturning is controlled by ensuring adequate resisting moment and an acceptable compression distribution. A simple ratio is

but a ratio alone does not replace checks on eccentricity, uplift, bearing pressure, and structural connection. Under cyclic or seismic actions, rocking and uplift may be intentional in some systems, but they require a code-based dynamic analysis.

5. Selection and design of shallow foundation types

Isolated pad foundations

An isolated footing supports one column. A preliminary area is obtained from service loading:

The footing is then proportioned to satisfy eccentricity, bearing pressure, settlement, sliding, and structural checks. Reinforced-concrete design includes bending moments, one-way shear, punching shear around the column, development length, cover, and durability. The column should be located so that the resultant load lies within the intended pressure zone.

Strip foundations

A strip footing supports a wall or closely spaced line of columns. Design is usually performed per metre run, with L = 1.0 m. Strip footings are efficient for load-bearing walls and relatively uniform soil. Longitudinal continuity, wall eccentricity, drainage, and local weak zones must be considered.

Combined footings

A combined footing supports two or more columns when columns are close together, an exterior column is near a property boundary, or individual footings would overlap. The resultant of column loads should be positioned near the centroid of the footing area to achieve a desirable pressure distribution. A rectangular combined footing is often designed so that its centroid aligns with the resultant column load, after which soil pressure, bending, and shear are checked.

Raft foundations

A raft supports several columns or walls over a large area. It is attractive where isolated footings would occupy a substantial fraction of the plan area, where differential settlement must be reduced, or where a stiff foundation can bridge moderate soil variability. A raft is not automatically a solution to weak soil: total settlement may remain excessive. Analysis may use rigid or flexible models, beam-on-springs idealizations, finite elements, or soil–structure interaction models. The model assumptions and stiffness of the raft must be compatible with the expected soil response.

6. Illustrative integrated case

Background. An illustrative two-storey masonry building has four exterior columns close to a property boundary and interior columns at regular spacing. The site contains 1.2 m of compacted granular fill over medium-stiff clay. Groundwater is 3.5 m below grade. Service column loads range from 350 to 700 kN, and wind produces moments at the exterior columns.

Problem. Preliminary isolated footings for exterior columns extend beyond the boundary. The design must avoid encroachment, control differential settlement, and resist wind-induced eccentricity.

Analysis. The investigation confirms that the fill is competent only where properly compacted; the clay governs long-term settlement. Service actions are used for settlement, while factored combinations are used for ULS in accordance with the selected code. Exterior column eccentricity produces a nonuniform pressure distribution, so the condition e ≤ B/6 is checked. Sliding is modest, but passive resistance is excluded because future excavation beside the boundary is possible.

Approach and solution. Interior columns retain isolated pads. Each exterior column is connected to its adjacent interior column by a reinforced-concrete strap beam, producing a strap footing whose resultant is shifted inward. Where column spacing makes the strap inefficient, a combined footing is used. Settlement is estimated using the clay compressibility data, and a raft alternative is compared economically. The final arrangement uses combined and isolated footings because it reduces excavation and satisfies the predicted differential-settlement criterion without requiring a full raft.

Outcome. The design documentation records load combinations, groundwater assumptions, effective parameters, pressure diagrams, settlement predictions, reinforcement checks, and construction tolerances. During construction, inspection confirms fill compaction and founding level; unsuitable pockets are removed and replaced under engineer-approved procedures.

Learning points. Property constraints can control foundation type. ULS and SLS may lead to different governing dimensions. Excluding unreliable passive resistance can change the preferred detail. Ground verification during construction is part of design risk management, not an optional administrative task.

7. Construction, risk, and professional practice

Good design includes constructability. Foundations should be placed on cleaned, undisturbed or properly improved bearing strata. Excavations require safe battering, shoring, access, and groundwater control. Concrete should not be placed on softened or ponded soil. Temporary dewatering must consider piping, basal instability, settlement of adjacent ground, and environmental discharge requirements.

Common errors include using ultimate loads with allowable pressure, ignoring footing self-weight, mixing gross and net bearing capacity, assuming laboratory strength represents the whole site, neglecting differential settlement, and relying on passive resistance that construction will remove. Another frequent error is treating a spreadsheet result as more reliable than the ground model.

Codes and regulations govern design combinations, partial factors, concrete detailing, seismic requirements, excavation safety, accessibility, environmental protection, and quality assurance. The applicable national standard must always control. Ethical practice requires transparent assumptions, competent review, conservative treatment of uncertainty where consequences are high, and prompt communication of unexpected ground conditions.

Digital tools and AI can assist with load schedules, sensitivity studies, settlement plotting, GIS integration, and inspection records. They cannot replace ground investigation, engineering judgment, code interpretation, or responsibility for the design. Automated results should be independently checked with hand calculations and dimensional reasoning.

Chapter Summary

Foundation design translates structural actions and a geological model into a safe, serviceable, and buildable support system. ULS checks bearing capacity, sliding, overturning, uplift, and structural resistance; SLS checks total and differential settlement, rotation, and usability. Eccentric loading is evaluated through moments, eccentricities, pressure distributions, or effective dimensions. Bearing capacity depends on strength, surcharge, footing geometry, embedment, load inclination, and the selected failure model. Isolated, strip, combined, and raft foundations serve different column arrangements and ground conditions. A reliable design uses consistent load and resistance formats, explicit assumptions, compatible soil parameters, code-based factors, construction verification, and professional judgment.

Key Terms

Bearing capacity: Maximum soil resistance that can be mobilized beneath a foundation before a specified failure condition.

Combined footing: A footing supporting two or more columns.

Contact pressure: Stress transmitted between the foundation base and supporting soil.

Differential settlement: Difference in settlement between two points of a structure.

Eccentricity: Distance between the load resultant and the centroid of the footing area.

Effective area: Reduced footing area used to represent eccentric loading.

Effective stress: Total stress minus pore-water pressure.

Factor of safety: Ratio of resistance or failure capacity to applied demand in an allowable-stress framework.

Foundation: Structural element that transfers load to soil or rock.

General shear failure: Bearing failure with a continuous mechanism and pronounced ground heave.

Isolated footing: Foundation supporting a single column.

Limit state: Condition beyond which safety or serviceability requirements are not satisfied.

Net pressure: Applied pressure considered relative to the removed or existing overburden pressure.

Punching shear: Localized shear failure around a concentrated column or loaded area.

Raft foundation: Large foundation supporting multiple columns or walls over much of a building plan.

Settlement: Downward movement of a foundation or ground surface.

Shallow foundation: Foundation transferring load mainly through near-surface soil.

Strip footing: Continuous footing supporting a wall or line of columns.

Ultimate limit state: State associated with collapse or loss of overall structural or geotechnical resistance.

Review Questions

5 Short Answer Questions

1. Distinguish ultimate limit state from serviceability limit state in foundation design.
2. What information is required from a ground investigation before sizing a shallow footing?
3. Define footing eccentricity and state the significance of the condition e ≤ B/6.
4. Name the three principal bearing-failure modes.
5. Why should passive resistance sometimes be excluded from a sliding check?

5 Long Answer Questions

1. Explain the complete workflow from structural actions and ground investigation to selection and verification of a shallow foundation.
2. Describe the assumptions and limitations of the classical bearing-capacity equation.
3. Compare isolated, strip, combined, and raft foundations, including typical applications and disadvantages.
4. Explain the components of foundation settlement and discuss how differential settlement affects buildings.
5. Compare allowable-stress design with partial-factor or load-and-resistance-factor design.

3 Analytical / Application Questions

1. A rectangular footing carries a vertical load and a moment about its width axis. Develop the contact-pressure calculation, determine whether tensile contact would occur, and explain how the design should change if e > B/6.
2. A proposed isolated footing satisfies bearing capacity but exceeds the project settlement criterion. Evaluate at least three technically different redesign options and state what additional ground information would guide the choice.
3. For a boundary column with substantial eccentricity, compare an enlarged isolated footing, a strap footing, and a combined footing. Recommend one approach and justify it using bearing pressure, constructability, structural action, and property constraints.

Multiple Choice Questions with Answers

Question 1

Which condition is primarily checked at the serviceability limit state?

A. Total and differential settlement

B. Ultimate punching collapse only

C. Nominal concrete cover only

D. Theoretical soil classification only

Correct Answer: A. Total and differential settlement

Question 2

For one-way eccentric loading, the no-tension condition for a footing of width B is generally expressed as:

A. e ≤ B/6

B. e ≤ B/2

C. e ≤ B

D. e ≥ B/6

Correct Answer: A. e ≤ B/6

Question 3

If a footing carries N = 600 kN over an area of 3 m², its average gross contact pressure is:

A. 50 kPa

B. 180 kPa

C. 200 kPa

D. 1,800 kPa

Correct Answer: C. 200 kPa

Question 4

Which factor is included in the classical drained bearing-capacity equation?

A. Nq

B. Only Poisson’s ratio

C. Only concrete tensile strength

D. Only groundwater temperature

Correct Answer: A. Nq

Question 5

The effective-area method for a rectangular footing with eccentricities eB and eL uses:

A. B' = B + 2eB and L' = L + 2eL

B. B' = B − 2|eB| and L' = L − 2|eL|

C. B' = eB/B and L' = eL/L

D. B' = BL and L' = B/L

Correct Answer: B. B' = B − 2|eB| and L' = L − 2|eL|

Question 6

Which foundation commonly supports a single column?

A. Isolated pad footing

B. Raft foundation only

C. Retaining wall only

D. Piled wharf only

Correct Answer: A. Isolated pad footing

Question 7

For rapid loading of saturated clay, which idealization may be appropriate when undrained strength governs?

A. Total-stress analysis with φu approximately zero

B. Drained sand analysis with zero unit weight

C. Elastic analysis with zero load

D. Rock mechanics analysis with no strength

Correct Answer: A. Total-stress analysis with φu approximately zero

Question 8

A combined footing is especially useful when:

A. An exterior column is close to a property boundary

B. There are no columns or walls

C. The soil has no bearing resistance at all

D. Only roof drainage is being designed

Correct Answer: A. An exterior column is close to a property boundary

Question 9

If resisting moment is 900 kN·m and overturning moment is 300 kN·m, the simple overturning ratio is:

A. 0.33

B. 1.5

C. 3.0

D. 1,200

Correct Answer: C. 3.0

Question 10

Why must gross and net bearing-pressure conventions not be mixed?

A. They use different reference pressures and can produce inconsistent resistance checks

B. They always have different units

C. Net pressure applies only to concrete strength

D. Gross pressure cannot be measured

Correct Answer: A. They use different reference pressures and can produce inconsistent resistance checks