### Introduction

The lowest part of every structure is referred to as the foundation. Its function is to transmit all the loads from the superstructure to the underlying soil on which it rests. A properly designed foundation will transfer the loads to the soil without overstressing the soil which in turn could cause either excessive settlement or shear failure of the soil. In-order to avoid overstressing the soil geotechnical engineers and structural engineers must determine the bearing capacity of the soil upon which the structure is to be founded. This applies to all forms of foundation, from a simple pad footing to a pile cap. The bearing stress capacity of the soil is the key variable that has a direct impact on the form and size of foundations. This post explains the principles of how

### Design Principles

The bearing capacity of a soil is dependent upon its structure, moisture content and the type of foundation that is placed upon it. It is important therefore to be familiar with the various types of soil that can be encountered. From simply knowing the soil type, it is possible to develop reasonable design solutions for any given sub-structure.

#### Foundation Types

There are four core types of foundations that are used within sub-structures. Most are built using concrete, both mass and reinforced, but it is possible to use steel sections as piles. * Figure 1 *shows these types of foundations.

#### Eurocode Methodologies of Assessing Bearing Capacity

Geotechnical engineering has a reputation of being imprecise and the design of it structures is practiced as an art rather than a science due to the varying nature of soils and it interactions with the substructures placed upon it. To counter this BS EN 1997-1 – Eurocode 7: Geotechnical Design – Part 1 General Rules describes the four differing methods that can be applied to the properties of soil. All of them are equally valid, with the major difference being that some produce more efficient solutions than others due to greater degrees of accuracy of modelling the soil conditions.

##### Geotechnical Design by Calculation

This method is reliant on the quality of data retrieved from geotechnical investigations carried out on the prospective site. Assumptions are made based on this data and in some instances simplifications will need to be applied to the calculation model that can lead to conservative results. For more details on this method see Clause 2.4 of BS EN 1997-1.

##### Geotechnical Design based on load tests and experimental models

In addition to geotechnical investigations that focus on the soil type and location of the water table, it is possible to carry out tests to determine the soil’s bearing capacity. These tests provide unique results for that particular site and thus are more accurate than making assumptions based on data collected from a standard investigation. This approach typically results in economical design solutions due to the accuracy of the data. Load tests however need to be at the correct scale to ensure the test mirrors the proposed foundation, which can prove to be expensive. See Clause 2.6 of BS EN 1997-1.

##### Geotechnical Design by Observation

In instances where it is not possible to predict how the soil will interact with a proposed substructure, it is possible to apply an observational based method of design. This requires the design of the substructure to be altered as new data is revealed about the soil during the construction of the foundations. Careful monitoring is needed throughout the construction process, as well as quick responses to the data being delivered, in order to prevent delays during the substructure works. This method is unlikely to provide a practical approach to the majority of foundation designs and is not recommended for designing substructures for buildings. For a more comprehensive description see Clause 2.7 of BS EN 1997-1.

##### Geotechnical Design by Prescription

In instances where the soil conditions of the site are well known, it is possible to prepare a set of parameters against which any sub-structure can be designed. Due to the generalised nature of this method, it’s common for it to produce conservatively designed solutions. For more information see Clause 2.5 of BS EN 1997-1.

#### Determining Undrained Soil Bearing Capacity

BS EN 1997-1 states that the ultimate bearing resistance of the soil must be greater than the applied bearing pressure from the substructure. In numerical terms this is expressed thus:

Where:

- Vd is the design vertical load, that is acting normal to the foundation’s base.
- Rd is the design bearing resistance of the soil

There are two equations for calculating base bearing capacity of a given soil. They are dependent on the condition of the soil, which is referred to as ‘drained’ or ‘un-drained’. For cohesive soils such as clay, un-drained design approach applies when placed under a short term load, as the force would be resisted by pore pressure rather than the grains that form the soil.

For un-drained soil Rd is defined thus:

Where:

- A’ is the effective base area of the foundation
- Cu;d is the design un-drained shear strength
- bc is the base inclination factor, if it is placed on sloping ground
- Sc is the shape factor of the foundation
- ic is the load inclination factor
- q is the overburden pressure at the base of the foundation

The effective area is based on how the load is applied to the foundation. If the load is eccentric to the centre of the foundation, then the area over which the load is applied to the soil from the foundation, is reduced. For the purposes of this note however, the assumption of all loads acting normal to the base with no eccentricity, will be made.

The design un-drained shear strength is defined as:

Where:

- cu;k is the undrained shear strength of the soil, which is a measured property
- γuc is the partial factor for the undrained shear strength

The overburden pressure q is the vertical effective weight of the soil that is located above the strata level where the foundation is to be installed. This post does not cover bases on inclined slopes for the sake of simplicity. Hence the base inclination and load inclination factors are not discussed.

#### Determining Drained Soil Bearing Capacity

In the case of drained soils, reliance can be placed on the friction between the particles within the soil. As such the equation for determining bearing capacity includes the factors that are influenced by the angle of friction (φ)

For drained soil, Rd is defined thus:

Where:

c’d is the design effective cohesion- q’ is the overburden pressure at the base of the foundation
- γ’ is the effective weight density of the soil at the strata level of the foundation
bc , bq and bγ are base inclination factorssc , sq and sγ are shape factors – see1 for derivation*Table*-
Nc , Nq and Nγ are the bearing capacity factors**(Table 2)**

#### Partial factors to soil properties

BS EN 1997-1 requires all material properties of soils to have a partial factor applied to them. This is due to the adoption of limit state theory to the design of substructures. There are two sets of factors that need to be applied to the material based on the applied load combination that is being considered. The following load combinations are to be used:

**Combination 1**: Permanent load x 1.35 + Variable load x 1.5 matched with set ‘M1’ properties. This is described as Set B in BS EN 1990

**Combination 2: **Permanent load x 1.00 + Variable load x 1.3 matched with set ‘M2’ properties. This is described as Set C in BS EN 1990.

The load set providing the worst condition is deemed to be the design case. ** Table 3** lists the values of the partial factors for material properties mentioned in this note

*This partial factor is applied to φd using the following equation:

All other partial factors are applied as a denominator for the relevant soil properties.

#### Displacement and settlement of foundations

In addition to determining the design bearing capacity of

As a general rule, if the ratio of design bearing capacity against the applied characteristic load is equal to or greater than 3, then no assessment of settlement is required. Note that this rule only applies to clay soils.

If however, the loading parameters do not meet this criteria then a settlement analysis of the foundations are required. This is a complex task and as such is beyond the scope of this post.

### Worked Example

A pad foundation measuring 0.75m x 0.75m with a thickness of 500mm is to be placed on a site with a sand/gravel soil. The water table is 3m below ground level and footings are founded 1.5m below ground level. The load combinations onto the pad footing are 750 kN/m2 for Combination 1 and 385 kN/m2 for Combination 2. Determine whether the soil can accommodate this applied bearing pressure.

Soil Properties: φ’ = 30º, γ’ = 17 kN/m3, c’=0

Since the soil is cohesion less and water table is below the base of the footing we can assume a drained condition.

Therefore the bearing capacity of the soil is given as shown below when cohesion, c=0

**N:B The base factors do not apply because the base is horizontal, and the inclination factors do not apply as well since the load is not applied at an angle**.

**Combination 1**

**Combination 2**

Therefore the applied pressure is within the allowable bearing pressure of the soil.

#### Further Reading & References.

*Tomlinson, M. J. (2001) Foundation Design and Construction 7th ed. New Jersey: Prentice Hall.*

*The Institution of Structural Engineers(2012)-Bearing Capacity: Technical Guidance Notes (level2)*

Braja M Das & Khaled Sobhan (2018)- Principles of Geotechnical Engineering 8ed.

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