This preview shows pages 1–2. Sign up to view the full content.
Application Example 14
(FOSM analysis for functions of many variables)
PROBABILISTIC ANALYSIS OF FOUNDATION
SETTLEMENT
Mechanical Model
Consider a footing resting on a compressible soil stratum of depth z
0
. Below z
0
, the soil
may be considered incompressible (e.g. there is bedrock or the stresses induced by the
foundation are small enough that soil deformation may be neglected).
An important
problem is to evaluate the amount of settlement.
The total settlement D may be found by adding the vertical strain of the soil
elements along the vertical line through the center of the footing.
This gives
z
o
D
=
∫
∆σ
(z)
dz
(1)
M( z)
0
where
∆σ
(z) is the increment in the vertical stress at depth z due to the foundation load
and M(z) is the elastic modulus of the soil at that depth (a deformability parameter of the
soil).
For simplicity, we divide the compressible soil stratum into n layers of equal
thickness (z
0
/n) and replace the integral in Eq. 1 with the discrete summation
n
D
=
z
o
∑
i
(2)
n
i
=
1
M
i
where
∆σ
i
=
∆σ
(z
i
), M
i
= M(z
i
), and z
i
= (i  0.5) z
0
/n is the average depth of layer i. If
the footing is circular of radius R and the load per unit area transmitted by the footing is
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Fall '07
 DonHill

Click to edit the document details