CALCULATION OF ULTIMATE LOAD ON PILE: PART 1 - ANALYTICAL METHOD

There are two standard ways to estimate the capacity of the pile (Coduto, 2001).

1. Static or dynamic pile load test

2. Analytical method

ANALYTICAL METHODS

Analytical methods are commonly performed by empirical method, p-z analysis, or both. For example, in a commercial software suite, the designer can employ an empirical method for initial design and use detailed p-z analysis for checking.

Empirical Methods

The load-carrying capacity of piles depends not only on soil types but also on construction methods. Therefore, many empirical formulas based on full-scale tests of piles have been proposed and applied to the different types of pile constructions.

Vertical load acting on the pile is transferred through the soil stratum utilizing side friction and toe bearing. The following equation expresses the ultimate load of pile Pu:

(Eq. 1)

The empirical formulas relate toe bearing and side friction to its measurable properties, like friction angle (sands), relative density (sands), and undrained shear strength (clays), for example. Moreover, the level of vertical stress is crucial to the load carrying of the pile.

Toe Bearing:

The bearing capacity equation can compute the bearing capacity with modifications. The most crucial issue is that bearing of the pile mostly fails by punching shear, not general shear (Coduto,2001).

Several empirical formulas to compute qu were suggested for different types of pile construction. For example,

For drained analysis (c=0), i.e., sands, the value of qu can be computed from (Coduto,2001)

For most piles, the first term can be omitted (usually less than 1% error). Then, the value of Nq* can be obtained from the empirical charts. Some empirical charts for estimating Nq* in sands are shown below:

Coyle and Castello (1981)

Meyerhof (1976)

For total stress analysis (phi' = 0), i.e., clays, the calculation of qu is given by (NAVFAC DM7-2)

Side friction:

The value of soil-pile friction for the concrete pile is conservatively used as 70% of the soil's friction angle.

K varies from 0.5 to 1.0 to the at-rest value depending on the pile types and construction method (driving, drilling, or augering). Table 14.5 (Coduto) presents the value of K/Ko for various forms of pile construction.

Side friction is usually computed by using the Beta method (Eq. 1)for soils under drained conditions (all types) and the Alpha method for soil under undrained conditions (silts and clays).

The safe design value can be obtained from

(Eq. 2)

where Wp = weight of pile, and NF = negative skin friction

In the general case,

FS = 3.0 shall be used for pile without static load test data

= 3.5 or above shall be used when using the pile driving formula

= 2.0-2.5 can be used when a static or dynamic load test is performed

p-z analysis (introduction)

p-z analysis is performed by representing underlying soils as spring supports. This analysis method requires a reasonable assignment of the spring models and their parameters. Based on numerical methods like Finite Element Method or Finite Difference Method, the p-z analysis can give load-displacement curves, which are commonly nonlinear. Still, the effect of consolidation is usually excluded and must be performed separately. Commercial software like GEO5 (Fine Inc.) and RS Pile (Rocscience) can perform p-z analysis for an individual pile or pile group.

Pile analysis software by GEO5

REFERENCES

DP Coduto, Foundation Design: Principles and Practices, 2nd ed., Prentice Hall, 2001

BM Das, Principles of Foundation Engineering, 7th ed., Cengage Learning, 2011

NAVFAC DM7-2