Geotechnical Engineering

DHARM

686 GEOTECHNICAL ENGINEERING

Terzaghi recommends that the coefficient of sub grade reaction be taken to be constant

with respect to the depth for preconsolidated clays. For normally loaded clays and silts, Reese

and Matlock, and Vesic assume that it varies linearly with depth. The constant of proportion-

ality is termed the coefficient of soil modulus variation.

k = k′. z ...(Eq. 16.53)

where k = coefficient of subgrade reaction at depth z, and

k′ = coefficient of soil modulus variation

Units for k are N/cm^2 /cm or N/cm^3

Units for k′ are N/cm^3 /m.

These will be dependent upon the unconfined compression strength in the case of clays

and upon the density index in the case of sands. The values of k and k′ are best determined

from a full-sized pile load test.

For long flexible piles, the lateral deflection is very nearly zero for most of the length of

the pile and hence the length of the pile is not important.

Beam

Reaction is a function of

the deflections at all points

Elastic

medium

Reaction at any point is dependent

only on the deflection at that point

Closely

spaced

elastic

springs

(a) Beam on elastic foundation (b) Winkler’s hypothesis for soil

Fig. 16.19 Winkler’s hypothesis for a soil medium

For short piles, the flexural rigidity of the pile loses its significance, the pile tends to

rotate as a unit, acting somewhat as a rigid member.

Reese and Matlock use in their analysis the relative stiffness factor, T, which is the

ratio of the stiffnesses of the pile and of the soil:

T =

EI

k′

F

HG

I

KJ

1/ 5

...(Eq. 16.54)

They give the deflection, bending moment and the soil pressure for the pile in terms of

non-dimensional coefficients in the form of tables and graphs.

Broms (1964) gives an analysis for laterally loaded piles in cohesive soils. Detailed treat-

ment of these analyses is outside the scope of this book.

*16.9 BATTER PILES

Batter piles combined with vertical piles are most effective for resisting large horizontal thrusts.

Such combinations have been commonly used to support retaining walls, bridge piers and