Soil Bearing Capacity Worked Example

› Note 19  Level 1

40

TheStructuralEngineer November 2012

Technical Technical Guidance Note

Soil bearing capacity Introduction

When designing foundations for a structure there is a need to determine the bearing capacity of the soil. 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 Technical Guidance Note explains the principles of how bearing capacity of soils are determined and how it impacts on the design of foundations.

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• Design principles

• Applied practice

• Worked example

• Further reading

• Web resources

Table 1: Common types of soil and their bearing capacity characteristics Soil type

Description

Typical foundation

Rock

Most commonly has a high bearing capacity; its weakness lies with any fissures that exist within its make-up and its weathering state

Reinforced pad foundation that serves more to fix the substructure to the rock strata rather than spread its load

Gravel

These are non-cohesive course soils that tend to be mixed with sand. They have a high bearing capacity and low compressibility. The presence of ground water can reduce its bearing capacity by half and the soil’s relative density also has an impact on its bearing capacity

Pad foundations due to the high bearing capacity. Piling is rare in these types of soils as it is often not needed

Sand

Similar to gravel in many respects, sandy soils also have a high bearing capacity and low compressibility. Where it is loosely compacted however, there is a risk of significant settlement as load is applied. Like gravel, the presence of ground water has a detrimental effect on both the soil’s bearing capacity and relative density

Similar to gravel

Clay

Clays are soils that are made up of very small particles and are described as ‘cohesive’. They typically have a lower bearing capacity than non-cohesive soils and compress when placed under load, which can occur over a long period of time, causing settlement. This is countered when they are over-consolidated at which point their properties are very similar to that of sand. Water has a significant impact on clay soils with its properties sensitive to the level of moisture content

Pad foundations to light 1-2 storey structures and then piled foundations for all other forms of structure. In cases where settlement is undesirable e.g. extensions to existing structures, piling may be necessary

Silt

Silt have a relatively high bearing capacity when confined, but their underlying structure breaks down when exposed to water. Silts can retain volumes of water that can freeze, causing the soil to heave

It is rare for structures to be directly founded upon silt due to its unpredictable nature. When encountered, a piling solution is adopted that passes through the silt into a more solid strata

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. There are essentially five different types of soil and/or strata (some of which have further sub-divisions) that have an impact on the design of foundations. Table 1 summarises these soils.

Foundation types There are five 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.

Methods of assessing soil properties Geotechnical engineering has a reputation for being imprecise due to the variable nature of soil and its interaction with 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

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•

Figure 1 Typical types of foundation

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 by prescriptive measures 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. 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 based on 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. Regardless of the method of soil analysis adopted, all results must be interpreted by a suitably qualified geotechnical engineer, which can then be passed onto the designer of the substructure.

Determining un-drained soil design 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: (1)

Vd # R d 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:

Rd A' = (r + 2) c u;d $ b c $ s c $ i c + q

(2)

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:

c c u;d = cu:kcu

(3)

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 is the vertical effective weight of the soil that is located above the strata level where the foundation is to be installed. This note 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 design 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:

Rd 1 A' = c' d $ N c $ b c $ s c $ i c + q' $ N q $ b q $ s q $ i q + 2 $ c' $ B' $ N c $ b c $ s c $ i c

(4)

› Note 19  Level 1

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Technical Technical Guidance Note

TheStructuralEngineer November 2012

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 factors sc , sq and sγ are shape factors – see Table 2 for derivation Nc , Nq and Nγ are the bearing capacity factors (Table 3). They are the soil cohesion, vertical effective stress and buoyant density factors respectively Table 2: Shape factors for drained soil bearing capacity Foundation shape

Rectangle

Square or circle

Shape factor

Equation in degrees

sq

1 + (B’ / L’ ) sin φ’d

sγ

1 – 0.3 (B’/L’ )

sc

(sq Nq – 1)/(Nq – 1)

sq

1 + sin φ’d

sγ

0.7

sc

(sq Nq – 1)/(Nq – 1)

are load inclination factors

For the sake of simplicity the inclination of base and load are not considered here.

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. In the UK the following load combinations are 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 4 lists the values of the partial factors for material properties mentioned in this note.

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

*Note: B’ and L’ are effective width and length of the foundation and φ’d is the design value for the angle of friction of the soil.

Table 3: Bearing capacity factors φ’d (in degrees)

ic , iq and iγ

Nq

Nc

Nγ

0

1

5.14

0

16

4

11

1

18

5

13

2

20

6

14

3

22

7

16

5

24

9

19

7

26

11

22

10

28

14

25

14

30

18

30

20

32

23

35

27

34

29

42

38

36

37

50

53

38

48

61

74

40

64

75

106

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Table 4: Partial factors for soil properties Soil property

M1 factors

M2 factors

*γφ’

1

1.25

γc’

1

1.25

γcu

1

1.4

γqu

1

1.4

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.

Glossary and further reading Bearing pressure – The pressure on the ground resulting from applied loads.

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 note.

Bearing resistance – The capacity of soil to resist bearing pressure.

Eurocode 0.

Soil properties – Measured properties of soil based on geotechnical investigations.

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

The applicable codes of practice for determining bearing capacity of soil are:

Further Reading

Displacement and settlement of foundations

BS EN 1990 Eurocode 0: Basis of Design

In addition to determining the design bearing capacity of soil, it is also necesary to determine the settlement of the foundations. This is done by using serviceability limit state principles that rely on the application of characteristic loads.

BS EN 1997-1 Eurocode 7: Geotechnical Design – Part 1 General Rules

*This partial factor is applied to {' k using the following equation:

{' d = Tan -1 c

Tan {' k m c {'

Errata Technical Guidance Note 15, Level 1 – Moment distribution: The application of the spring support in the worked example was incorrectly modelled. The corrected analysis is shown in the following calculations and figures:

(5)

Applied practice

BS EN 1997-1 UK National Annex to Eurocode 7: Geotechnical Design – Part 1 General Rules

Overburden pressure – The pressure at which the level of the proposed foundation is to be founded at within the soil.

Tomlinson, M. J. (2001) Foundation Design and Construction 7th ed. New Jersey: Prentice Hall Eurocode 0.

Web resources

The Institution of Structural Engineers library: www.istructe.org/resources-centre/library