Design of Shallow Foundations - Theory & Concepts

Shallow Foundations

Shallow foundations transmit structural loads directly to the underlying soil at a relatively shallow depth (typically defined as depth

D_f \le B

). They are the preferred and most economical choice when the surface soil layers possess sufficient bearing strength and stiffness.

Types of Shallow Foundations

The appropriate type of shallow foundation depends on the column spacing, the magnitude of loads, and the properties of the underlying soil.

Common Foundation Types

Isolated (Spread) Footing: Supports a single column. It is the most basic, common, and economical foundation type, used when columns are spaced relatively far apart and soil is competent.

Combined Footing: Supports two or more closely spaced columns. This is specifically used when isolated footings would overlap, or when an exterior column is located directly on a property line (preventing an isolated footing from being centered under the column).

Strap (Cantilever) Footing: Consists of two separate isolated footings connected by a massive, rigid structural beam (the strap). It is used to transfer bending moments when the distance between an eccentrically loaded edge column and an interior column is too large for a standard combined footing.

Mat (Raft) Foundation: A large, heavily reinforced continuous concrete slab that supports the entire building superstructure. It is utilized when soil conditions are erratic/soft (to minimize differential settlement) or when the required area for isolated footings exceeds 50% of the building's total footprint.

General Structural Design Steps

Designing a concrete foundation requires a careful interplay between geotechnical engineering (assessing the soil) and structural engineering (designing the concrete and steel).

The Design Process

Determine Footing Plan Area: Sizing the footprint is a geotechnical check based on the Allowable Soil Bearing Capacity ( $q_{all}$ ) using Unfactored Service Loads (Dead Load + Live Load).

Required Footing Area

Minimum plan area needed to distribute the service load within the allowable soil bearing capacity; sized using unfactored loads.

A_{req} = \frac{P_{service}}{q_{all}}

Variables

Symbol	Description	Unit
$A_{req}$	Required plan area of the footing	-
$P_{service}$	Total unfactored service load (e.g., Dead + Live Load)	-
$q_{all}$	Allowable soil bearing capacity	-

Determine Footing Thickness ( $h$ ): The depth of the concrete is governed by shear strength checks using Factored Loads (e.g., $1.2D + 1.6L$ in LRFD). The footing must resist two types of shear:
- One-Way (Beam) Shear: Evaluated at a critical section located at a distance $d$ from the face of the column.
- Two-Way (Punching) Shear: Evaluated at a critical perimeter located at a distance $d/2$ from the face of the column.
Determine Flexural Reinforcement: Based on the maximum bending moment calculated at the face of the column, using Factored Loads.

Important

Always remember: Service Loads are used to determine the size of the footing (to satisfy geotechnical soil pressure limits). Factored Loads are used to design the concrete thickness and steel reinforcement (to satisfy structural codes like ACI 318 or NSCP).

Design Principles for Combined Footings

The fundamental goal when designing a combined footing is to achieve a uniform soil pressure distribution to prevent the footing from tilting.

Rectangular Combined Footing

To achieve uniform soil pressure, the geometric centroid of the footing area must align perfectly with the resultant force of the column loads.

Locate Resultant: Calculate the magnitude of the Resultant force ( $R = P_1 + P_2$ ).
Find Resultant Location: Take moments about the exterior column to find the distance to the Resultant ( $x_R$ ).
Size Length ( $L$ ): Set the footing length so its center is exactly at $x_R$ . Thus, $L = 2(x_R + \text{edge distance})$ .
Size Width ( $B$ ): Calculate the width using $B = A_{req} / L$ .

Note: If the required $L$ is physically impossible due to site constraints, a Trapezoidal combined footing must be used.

Mat Foundations

Mats distribute heavy column loads over a massive area, significantly reducing the bearing pressure compared to isolated footings.

Modulus of Subgrade Reaction ( $k_{s}$ )

For the structural design of flexible mat foundations, the soil is commonly modeled mathematically as a bed of independent elastic springs (Winkler foundation model). The stiffness of these springs is the modulus of subgrade reaction.

Modulus of Subgrade Reaction

Spring stiffness of the soil per unit area used in the Winkler (beam-on-elastic-foundation) model for structural design of mat foundations.

k_s = \frac{q}{\Delta}

Variables

Symbol	Description	Unit
$k_{s}$	Modulus of subgrade reaction	-
$q$	Soil contact pressure	-
$\Delta$	Corresponding settlement	-

$k_s$ is not a fundamental soil property. It depends heavily on the size of the loaded area.
A small plate load test value must be corrected (scaled down) for a massive mat foundation.

Compensated (Floating) Foundation

A sophisticated geotechnical technique used for building heavy structures on extremely soft, highly compressible clays.

Net Bearing Pressure (Compensated)

Net pressure increase on the underlying soil from a compensated (floating) foundation; ideally approaches zero to minimize consolidation settlement.

q_{net} = q_{building} - \gamma D_f \approx 0

Variables

Symbol	Description	Unit
$q_{net}$	Net increase in bearing pressure	-
$q_{building}$	Gross pressure exerted by the building	-
$\gamma$	Unit weight of the excavated soil	-
$D_{f}$	Depth of excavation	-

Mechanism: The foundation is excavated so deep that the weight of excavated soil offsets the new building weight.
Result: Net effective stress increase is negligible, practically eliminating consolidation settlement.

Interactive Shallow Foundation Design

Experiment with different shallow foundation sizes and loads to understand settlement and bearing capacity.

Shallow Foundation Sizing & Pressure

Axial Load,

P

(kN): 1000

Overturning Moment,

M

(kN·m): 0

Allowable Bearing,

q_{all}

(kPa): 150

Required Square Width (

B

)

0.0 m

Maximum Soil Pressure (

q_{max}

)

0.0 kPa

Eccentricity (

e = M/P

)

0.00 mLimit

B/6

: 0.00 m

The simulator automatically increases the footing width ( $B$ ) until the maximum soil pressure ( $q_{max}$ ) is below the allowable bearing capacity. When a moment is applied, the pressure becomes trapezoidal. If eccentricity ( $e$ ) exceeds $B/6$ , tension develops at the heel (shown as $q_{min} = 0$ ).

Floating Foundations and Compensated Rafts

A specialized technique for constructing heavy buildings over extremely soft soils where deep foundations are impractical or prohibitively expensive.

Compensated Rafts

The principle is based on Archimedes' buoyancy: If you excavate an enormous mass of soil (the weight of the excavated soil equals the weight of the new building), the net stress increase on the deep soft soil beneath the raft is essentially zero.
Fully Compensated (Floating) Foundation:

Fully Compensated Foundation

Ideal condition for a floating foundation where the weight of excavated soil exactly offsets the new building weight, producing zero net stress increase.

W_{building} = W_{excavated\_soil}

Variables

Symbol	Description	Unit
$W_{building}$	Total weight of the new building structure	-
$W_{excavated\_soil}$	Total weight of the soil removed from the excavation	-

Partially Compensated Foundation: The building weight exceeds the excavated soil weight, but the net stress increase is kept small enough to limit settlement to tolerable amounts.
Critical consideration: Construction requires massive, deep excavations with extensive bracing and dewatering, which can induce ground movements affecting adjacent structures.

Key Takeaways

Shallow foundations safely distribute concentrated structural loads over a sufficient area ( $A$ ) so that the applied pressure ( $P/A$ ) does not exceed the soil's allowable bearing capacity ( $q_{all}$ ).
Isolated footings are the industry standard for individual columns. Combined footings are required when isolated footings would physically overlap or when dealing with property-line columns.
Mat foundations are essentially large slabs that bridge over localized weak spots, drastically minimizing differential settlement. Structural design often models the soil using the Modulus of Subgrade Reaction ( $k_s$ ).
Critical Design Rule: Sizing the foundation footprint uses Unfactored Service Loads, whereas designing the concrete thickness and steel rebar uses Factored Loads (LRFD).
Shear strength (specifically two-way punching shear) almost always dictates the required thickness of a concrete footing.

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Shallow Foundations

Types of Shallow Foundations

Common Foundation Types

General Structural Design Steps

The Design Process

Required Footing Area

Important

Design Principles for Combined Footings

Rectangular Combined Footing

Mat Foundations

Modulus of Subgrade Reaction (ksk_sks​)

Modulus of Subgrade Reaction

Compensated (Floating) Foundation

Net Bearing Pressure (Compensated)

Interactive Shallow Foundation Design

Shallow Foundation Sizing & Pressure

Floating Foundations and Compensated Rafts

Compensated Rafts

Fully Compensated Foundation

Modulus of Subgrade Reaction ( $k_{s}$ )