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Hubbell # Using Terzaghi’s Equation in Foundation Design Featured

Theoretical models to predict the capacity of helical piles are based on Soil Mechanics and an appropriate mechanism of failure, depending on the geometry of the pile/anchor and the type of soil. Using a soil mechanics approach requires determination of soil properties such as shear strength and unit weight as well as information about the location of the water table.

*This is a Chance Foundation Solutions story written by Gary L. Seider, PE., Engineering Manager, Civil & Utility Helical Products. *

When possible, high quality measurements of soil properties from either laboratory tests on undisturbed samples or appropriate in situ tests will be needed. Alternatively, soil properties might be estimated by a common field test, such as the Standard Penetration Test (SPT) or the Cone Penetration Test (CPT) , to make use of available project information . The design approach used for helical piles and anchors makes use of the basic General Bearing Capacity Equation (GBCE), which was developed in the 1940s by Terzaghi. However, adjustments to the equation may be applied as appropriate to the soil type, which is also done for regular deep foundations. The GBCE includes three terms, all of which are related to soil properties.

The following is Terzaghi’s general bearing capacity equation, which is used to determine the ultimate capacity of soil (Q_{ult}, a.k.a Q_{H}).

**Q _{ult} = A_{h}(c’N_{C} + q’N_{q} + 0.5γ’BN_{γ})**

where:

- A
_{h}= Projected helix area - c = soil cohesion
- q’ = effective overburden pressure
- B = Footing width (base width)
- γ’ = effective unit weight of the soil

N_{C}, N_{q}, N_{γ} = bearing capacity factors

This General Bearing Capacity Equation for shallow and deep foundations in soils can be found in every Foundation Engineering textbook and represents the traditional approach to the design of foundations under compression loading. In order to make use of this equation for the design of helical piles, some adjustments are necessary, depending on the geometry of the pile or anchor and the direction of loading, i.e., compression or tension. This equation is an Effective Stress Analysis (ESA) and assumes fully drained loading. This assumption only applies to sands and other freely draining materials. In clays, it is assumed that the loading is applied sufficiently fast so that the soil responds in an undrained manner. We then use a Total Stress Analysis (TSA ) for this case.

Terzaghi’s Shallow Foundation Bearing Capacity Factors [Bowles (1988) and ASCE (1993a)]

φ ’ | N_{C} | N_{γ} | N_{q} |

0 | 5.7 | 0 | 1 |

10 | 9.6 | 1.2 | 2.7 |

12 | 10.8 | 1.7 | 3.3 |

14 | 12.1 | 2.3 | 4 |

16 | 13.7 | 3 | 4.9 |

18 | 15.5 | 3.9 | 6 |

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 | 27.9 | 28.5 |

34 | 52.6 | 36 | 36.5 |

36 | 63.5 | 52 | 47.2 |

38 | 77.5 | 80 | 61.5 |

40 | 95.7 | 100.4 | 81.3 |

42 | 119.7 | 180 | 108.7 |

44 | 151.9 | 257 | 147.7 |

46 | 196.2 | 420 | 204.2 |

48 | 258.3 | 780.1 | 287.8 |

Following is based on Bowles (1988) concerning the use of Terzaghi’s general bearing capacity equation for deep foundations where the various terms of the bearing capacity equation are distinguished.

- The cohesion term predominates in cohesive soil.

- The depth term (q’N
_{q}) predominates in cohesionless soils. Only a small increase in D (vertical depth to footing or helix plate) increases Qult

- The base width term 0.5γ ’BN
_{γ}provides some increase in bearing capacity for both cohesive and cohesionless soils. In cases where B < 3 to 4 m (9.8 to 13.1 ft), this term could be neglected with little error.

The base width term of the bearing capacity equation is not used when dealing with helical piles/anchors/piles because, as Bowles indicates, the resulting value of that term is quite small. The effective overburden pressure (q’, of consequence for cohesionless soils) is the product of depth and the effective unit weight of the soil. The water table location may cause a reduction in the soil bearing capacity. The effective unit weight of the soil is its in-situ unit weight when it is above the water table. However, the effective unit weight of soil below the water table is its in-situ unit weight less the unit weight of water.

Notes on use of Terzaghi’s Bearing Capacity equation:

- Because helix plates are generally round, Terzaghi’s adjustment for circular footings is sometimes used for compression loading: Q
_{ult}= A_{h}(1.3cN_{C}+ γ’N_{γ}+ 0.3γ’BN_{γ})

- Because B is considered very small for helical piles and anchors, relative to most concrete footings, most engineers choose to ignore the term 0.5γ’BNg in design.

- 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) £ 0

- 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.

- For saturated clay soils, Nq = 1.0; For sands, Nq is a function of the friction angle, φ’.

- For square-shaft piles/anchors manufactured by Hubbell Power Systems, Inc., the side resistance is generally ignored. For round-shaft piles/anchors there may be a component of side resistance that contributes to capacity depending on the configuration of connections between extension sections.

- In all cases, for both compression and tension loading, the upper limit of capacity is governed by the structural capacity of the pile/anchor as provided by the manufacturer. See section 7 of the CHANCE Technical Design Manual for structural capacity ratings of CHANCE helical piles.

DOWNLOAD THE TECHNICAL DESIGN MANUAL

There is cause for concern when a helical pile installation is terminated in sand above the water table with the likelihood that the water table will rise with time to be above the helix plates. In this situation, the helical pile/anchor lead section configuration and depth should be determined with the water at its highest anticipated level. Then the capacity of the same helical pile should be determined in the same soil with the water level below the helical pile. This will typically produce higher load capacities and a more difficult installation, i.e., it will require more installation torque. In some cases, a larger helical pile/anchor product series, i.e., one with greater torque capacity, must be used to enable installation into the dry conditions.

For more information on Terzaghi’s equation or helical pile foundation design, download the CHANCE Technical Design Manual or contact your local distributor.

Compared to other deep foundation technologies, CHANCE helical piles have the advantage of decades of research and testing that allows engineers to be able to confidently predict the ultimate capacity of a helical pile design.References:

- Bowles, J.E., Foundation Analysis and Design, Fourth edition, McGraw-Hill, 1988.
- Skempton, A. (1951): The bearing capacity of clays. Proceedings of Building Research Congress, Division 1, Part III.

**Source: ** PROOF MATTERS: Using Terzaghi’s Equation in Foundation Design

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