## METHODS USING STATICS FOR DRIVEN PILES

**a-Method:**

Skin Friction:

The a-method is based on a total stress analysis (TSA) and is normally used to estimate the short-term load capacity of piles embedded in fi ne-grained soils. In the a-method, a coeffi cient, au, is used to relate the undrained shear strength, su, to the adhesive stress ( fs) along the pile shaft. The skin friction, Qf, over the embedded length of the pile is the product of the adhesive stress ( fs 5 ausu) and the surface area of the shaft (perimeter 3 embedded length). Thus

where j is the number of soil layers within the embedded length of the pile. For a cylindrical pile of uniform cross section and diameter D penetrating a homogeneous soil, Qf is given by

where L is the embedded length of the pile.

The value of au to use in determining the load capacity of piles is a subject of much debate and testing. Most tests to determine au are laboratory tests on model piles installed in a uniform deposit of soil. The major problems with these laboratory tests are:

1. It is diffi cult to scale up the laboratory model test results to real piles.

2. The soils in the fi eld are mostly nonuniform compared with carefully prepared uniform soils in the laboratory.

3. Pile installation in the fi eld strongly infl uences au, which cannot be accurately duplicated in the laboratory.

4. Undefi ned (peak or critical state and at what initial void ratio) values of su have been used in building relationships between su and au.

Full-scale fi eld tests on real piles are preferred, but such tests are expensive and the results may apply only to the site where the tests are performed. The results from cone penetrometers and the SPT have been linked to au, but these are found from statistical correlations with rather low coeffi cient of correlation.

Recall from Chapters 10 and 11 that su is not a fundamental soil property but depends mainly on the initial void ratio or initial confi ning pressure. Because pile installation changes the initial soil stress state in ways that we can predict, at least easily, the author recommends that su should correspond to the critical state value. Converting any known value of su to critical state value was presented in Chapter 11. Values for au given by Tomlinson (1987) are shown in Figure Randolph and Murphy (1985) recommended that fs be estimated using the lower of the following two expressions.

End Bearing The end bearing capacity is found by analogy with the conventional failure mode of shallow foundations and is expressed as

where fb is the base resistance stress, Nc is a bearing capacity coeffi cient, (su)b is the undrained shear strength of the soil at the base of the pile, and Ab is the cross-sectional area of the base of the pile. Several expressions have been proposed for Nc. In this textbook we will use the following expressions for Nc:

**b-Method:
Skin Friction:** The b-method is based on an effective stress analysis and is used to determine the short-term and long-term pile load capacities of coarse-grained soils and the longterm load capacity of fi ne-grained soils. The friction along the pile shaft is found using Coulomb’s friction law, where the frictional stress is given by fs 5 msrx 5 srx tan fri, and where m is the coeffi cient of friction, s9x is the lateral effective stress, and f9i is the interfacial effective friction angle. The skin friction is expressed as

We can replace the two coeffi cients K and tan f9i by a single factor b to yield

Recall from Chapter 7 that for normally consolidated fi ne-grained soils and coarse-grained soils,

and for overconsolidated fi ne-grained soils

The soil mass adjacent to a pile is expected to reach the critical state or close to it (Section 13.4). You should then use critical state shear strength parameters in determining the long-term load capacity of piles. Loose, coarse-grained soils adjacent to driven piles are densifi ed and f'= f'p. The actual value of f''depends on the magnitude of the normal effective stress. Since the magnitude of the normal effective stress is uncertain, you should be cautious in using f9p to estimate the long-term load capacity. It would be prudent to use f' =f'cs in all cases except for some overconsolidated clays with a predominance of parallel aligned particles, where it is advisable to use f'= f'r.

The value of b is also a subject of many debates, especially for coarse-grained soils. One reason for these debates is the correlation of b with undefi ned values of f'. In this textbook, we will use f'cs (a fundamental soil property) or f'r for overconsolidated clays with a predominance of parallel aligned platy particles. The following expressions for b are selected for this textbook.

**Fine-grained soils (Burland, 1973):**

**Coarse-grained soils:**

Typical ranges of values for f'i .The vertical effective stress, s'z, is calculated at the center of each soil layer.