Introduction to Foundation Engineering using Terzaghi’s Bearing Capacity Equation

Helical pile foundation design is an engineering science, thanks in part to the work of Austrian mechanical engineer Karl von Terzaghi. Learn more about using his equation in this introduction to foundation engineering.

The Chance Civil Construction team has created a guide to introduce students to the basics of geotechnical design of single-helix and multi-helix helical piles and helical anchors. It is intended as an introduction only and does not include all of the subtleties involved in detailed geotechnical or structural design procedures. The design methods given in this Guide and the sample problems presented are intended for instructional purposes only. This Guide only covers the design of helical piles and helical anchors installed in uniform soils and does not give design procedures for layered or stratified soil profiles. 

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Helical piles and helical anchors are generally classified as either “shallow” or “deep” depending on the depth of installation of the top helix below the ground surface, usually with respect to the helix diameter. There are some situations in which the installation may be considered partway between “shallow” and “deep”, or “intermediate”. In this Guide, only design procedures for “shallow” and “deep” installations will be described. Table 1 gives a summary of the most common design situations involving helical piles and helical anchors that might be encountered. Note that the use of “shallow” multi-helix anchors for either compression or tension loading is not a typical application and is not covered in this Guide.

Table 1. Typical Design Situations for Single-Helix and Multi-Helix Helical piles and Helical anchors. 

Single-Helix 

Multi-Helix 

Failure Condition 

Failure Condition 

Shallow 

Deep 

Shallow 

Deep 

Compression 

Tension 

Compression 

Tension 

Compression 

Tension 

Compression 

Tension 

Clay 

Clay 

Clay 

Clay 

N/A 

N/A 

Clay 

Clay 

Sand 

Sand 

Sand 

Sand 

N/A 

N/A 

Sand 

Sand 

Mixed Soils 

Mixed Soils 

Mixed Soils 

Mixed Soils 

N/A 

N/A 

Mixed Soils 

Mixed Soils 

Many helical piles and helical anchors are manufactured with square central shafts. For these piles/anchors, the contribution of the shaft to the ultimate capacity is usually ignored and the total capacity is only calculated from the bearing capacity of the helical plate(s). For helical piles and helical anchors with round steel central shafts the shaft between plates, in the case of multi-helix elements is ignored, but the shaft above the top plate may be included in design, at least for that section of the shaft in full contact with the soil. [Get the guide and read more about this in Section 4] 

At the present time, the design of helical piles and helical anchors generally follows the traditional theory of General Bearing Capacity used for compression loading of foundations. As applied to a single-helix helical pile or helical anchor, Terzaghi’s general bearing capacity equation for determining ultimate bearing capacity, as given in most Foundation Engineering textbooks, may be stated as: 

QH = AH(c’NC + q’Nq + 0.5g’BNg

where: 

QH = Ultimate Capacity 

AH = Projected Area of Helix 

c’ = cohesion 

q’ = effective overburden stress = g’D 

g’ = effective unit weight of soil 

D = depth 

B = diameter of helix 

NC, Nq, Ng = bearing capacity factors 

 

Table 2. Terzaghi’s Shallow Foundation Bearing Capacity Factors.  (from and Bowles (1988) and ASCE (1993a)) 

φ 

Nc 

Nγ 

Nq 

0 

5.7 

0.0 

1.0 

10 

9.6 

1.2 

2.7 

12 

10.8 

1.7 

3.3 

14 

12.1 

2.3 

4.0 

16 

13.7 

3.0 

4.9 

18 

15.5 

3.9 

6.0 

20 

17.7 

4.9 

7.4 

22 

20.3 

5.8 

9.2 

24 

23.4 

7.8 

11.4 

26 

27.1 

11.7 

14.2 

28 

31.6 

15.7 

17.8 

30 

37.2 

19.7 

22.5 

32 

44.0 

27.9 

28.5 

34 

52.6 

36.0 

36.5 

36 

63.5 

52.0 

47.2 

38 

77.5 

80.0 

61.5 

40 

95.7 

100.4 

81.3 

42 

119.7 

180.0 

108.7 

44 

151.9 

257.0 

147.7 

46

196.2

420.0

204.2

48

258.3

780.1

287.8

Adjustments or simplifications to the bearing capacity equation may be made as appropriate for application to the design situations given in Table 1. 

 

If you’re ready to start designing, check out HeliCAP® Helical Capacity Design Software. This free online program was developed to aid engineers in performing calculations on site soil parameters.  

CREATE ACCOUNT AND START USING HELICAP

 

Notes on use of Terzaghi’s Bearing Capacity equation: 

  1. Because helical plates are round, Terzaghi’s adjustment for round footings is sometimes used for compression loading: 
    QH = AH(1.3c’NC + q’Nq + 0.6g’BNg) 

  2. Because B is considered very small for Helical piles and Helical anchors, relative to most concrete footings, some engineers choose to ignore the term 0.5g’BNg in design.
     
  3. In saturated clays under compression loading, Skempton’s (1951) Bearing Capacity Factor for shallow round helical plates can also be used: 
    NC = 6.0(1 + 0.2D/B) £ 9.0 

  4. The unit weight of the soil is the total (wet) unit weight if the helical plate(s) is above the water table and the buoyant unit weight if the helical plate(s) is below the water table. 

  5. For saturated clay soils, Nq = 1.0; For sands, Nq is a function of the friction angle, φ’.
     
     
  6. For square-shaft Piles/Anchors, the shaft resistance is generally ignored. For round shaft Piles/Anchors there may be a component of shaft resistance that contributes to capacity depending on the configuration of connections between  
    extension sections. 

  7. In all cases, for both compression and tension loading, the upper limit of capacity is governed by the mechanical strength of the Pile/Anchor as provided by the manufacturer. 

  8. For multi-helix Helical piles and Helical anchors, most manufacturers produce sections with a helix spacing of 3 times the helix diameter and it is generally assumed that the individual helices act independent of each other, the ultimate capacity of a multi-helix Pile/Anchor is typically taken as:
    QM = SQH
    where:
    QM = Total Capacity of a Multi-Helix Pile/Anchor
    QH = Capacity of an Individual Helix 

  

Our engineering professionals have a vast wealth of experience designing foundations in all viable types of soil strata around the world. Contact our team with your questions or reach out to your local distributor for design assistance, product selection, and quotes.



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