Unit Skin Friction (Beta Method)

Unit shaft friction (beta method)

The unit shaft friction of a pile in granular soil, computed by the beta method, is f_s = β·σ'_v, obtained from the coefficient β and the effective vertical stress σ'_v at the depth being considered. The β method (or effective stress method) is the modern, rational way of estimating shaft friction for piles in granular soils (sands) and for clays expressed in effective-stress terms. It starts from the premise that friction along the pile shaft behaves like friction at any other interface: the shear stress equals the stress normal to the surface (the horizontal stress in the soil, K_s·σ'_v) times the tangent of the interface friction angle (tan δ). Lumping those two factors into a single coefficient, β = K_s·tan δ, the unit friction becomes simply β·σ'_v. In sands β typically ranges from 0.2 to 0.5, and it runs higher for driven piles, which raise K_s by displacing the surrounding soil. The great advantage of the β method is that it works from effective stress, which grows with depth, so it captures the fact that shaft friction increases as you go deeper — although there is a limit to that (the "critical depth", beyond which friction stops growing, a phenomenon still under debate). Integrating f_s times the perimeter over the pile length gives the total shaft resistance. Enter the beta coefficient and the effective vertical stress.