Application of the subset simulation approach to spatially varying soils - Risk and Reliability in Geotechnical Engineering - page 561

b

B = 7.5 b

Figure 15.4 Soil domain and mesh used in the numerical simulations.

where δ v max is a tolerable vertical displacement of the footing center and δ v is the vertical
displacement of the footing center due to the applied pressure q s . In this chapter, it was
assumed that δ v max / b = 2 × 10 −2 .
The deterministic model used to calculate the footing vertical displacement δv was
based on the commercial numerical code FLAC 3D . For this calculation, a footing of
breadth b that rests on a soil domain of width B and depth H was considered in the
analysis ( Figure 15.4 ).
An optimal nonuniform but symmetrical mesh composed of 750 zones was employed.
Although an SLS analysis is considered herein, the soil behavior was modeled by a conven-
tional elastic-perfectly plastic model based on Mohr-Coulomb failure criterion in order
to take into account the possible plastification that may occur near the edges of the foun-
dation even under the service load. On the other hand, the strip footing was modeled by
a linear elastic model. It is connected to the soil via interface elements that have the same
shear strength parameters as the soil. The values of the shear strength and elastic proper-
ties of the soil, footing, and interface are given in Table 15.7 . The soil unit weight is equal
to 18 kN/m 3 .
In order to calculate the footing vertical displacement for a given random field realization,
(i) the vertical and horizontal coordinates of the center of each element of the mesh were
calculated; then the K-L expansion was used to calculate the value of the Young's modulus
at the center of each element using Equation 15.11 , (ii) geostatic stresses were applied to the
soil, (iii) the obtained displacements were set to zero in order to obtain the footing displace-
ment due to only the footing applied pressure, and finally (iv) the uniform vertical pressure
was applied to the footing and the vertical displacement at the footing center due to this
pressure was calculated.

Table 15.7 Shear strength and elastic properties of soil, footing, and interface
Variable Soil Footing Interface

c 20 kPa N/A 20 kPa

30° N/A 30°

φ

20° N/A 20°

ψ = 2/3 φ

E 60 MPa 25 GPa N/A

0.3 0.4 N/A

ν

K n N/A N/A 1 GPa

K s N/A N/A 1 GPa