Civil Engineering Reference
In-Depth Information
4.4.1 Subgrade reaction approach
Early analysis of the response of piles to lateral loading treated the soil as a series of
springs down the length of the pile - the so-called Winkler idealization of soil (see
Figure 4.44). The spring stiffness,
k
, giving the load per unit length of pile induced for
unit lateral deflection of the pile, is generally referred to as the coefficient of subgrade
reaction. If
k
is assumed constant down the length of the pile, then analytical solutions
are possible, giving the deflected shape of the pile, and the shear force and bending
moment distribution down the pile (Matlock and Reese, 1960). For a pile of a given
bending rigidity,
EI
p
, in soil with a coefficient of subgrade reaction,
k
, there is a critical
length beyond which the pile behaves as if it were infinitely long.
This critical length is given by
4
(
EI
)
p
k
1
/
4
L
c
=
/
(4.68)
Thus, as for the case of long slender piles subjected to axial loading, the effects of load
applied at the top of the pile die out at some depth down the pile. In fact the large
majority of piles encountered in practice behave as 'flexible' piles (i.e. longer than their
critical length). For such piles, the deflection,
u
, and rotation,
θ
, at ground level due
to applied load,
H
, and moment,
M
, are given by
L
c
4
−
1
L
c
4
−
2
√
2
H
k
M
k
u
=
+
(4.69)
L
c
4
−
2
L
c
4
−
3
√
2
M
k
H
k
θ
=
+
Similar expressions for the critical length and for the load deformation response may
be obtained for cases where the value of the coefficient of subgrade reaction varies with
depth, in particular where it is proportional with depth (Reese and Matlock, 1956).
Figure 4.44
Subgrade reaction model of soil around pile.
