Civil Engineering Reference
In-Depth Information
13.2.2 Numerical methods
With the ever increasing ability of computers to perform com-
plex calculations at higher speeds, predicting soil-structure
displacements, soil stresses or forces within structural
elements using software packages is considered a standard
tool that has become increasingly the norm in engineering
design.
The range of available software packages is steadily grow-
ing and varies from relatively simple programmes that inte-
grate the sum of the values obtained from a simple formula
to three-dimensional finite element packages that can simulate
the interaction of complex foundation and substructure propos-
als. It is important that these packages are used to complement
the overall design process rather than in isolation to ensure that
a coherent solution is provided.
The three most common types of numerical methods adopted
in solving soil-structure interaction problems are:
δ
δ
Deflected wall shape rotated
through 90°
Deflected wall shape
Figure 13.4(a)
Theoretical ground settlement behind a cantilever wall
δ
/
2
elastic methods
■
spring models
■
finite element methods
■
δ
These are discussed further below.
13.2.2.1 Elastic methods
This approach assumes a methodology whereby a soil mass is
simulated using elastic theory and assigned a stiffness, gen-
erally taken as the Young's modulus. Pressures can then be
applied to the soil mass which then deforms by a magnitude
governed by the value of its assigned stiffness. Elastic soil
models are further discussed in Sections 13.4.1 and 13.4.2.
It should be noted that there are limitations to such methods
as they will not take into account issues such as the potential
stiffening effects resulting from soil surcharging, changes in
stiffness with time or the variation in soil stiffness with mag-
nitude of strain.
Deflected wall shape
Figure 13.4(b)
Theoretical ground settlement behind a propped
retaining wall
13.2.2.3 Finite element method
For more complex soil-structure interaction problems where
the soil mass is modelled in addition to the structural compo-
nents, finite element or finite difference techniques are used.
Such software packages allow construction sequences to be
simulated, predict adjacent soil and building displacements
and can account for consolidation and groundwater effects.
Two- and three-dimensional finite element software pack-
ages are becoming increasingly popular due to the develop-
ment of their user interfaces, making the overall modelling and
analysis process simpler. In theory, they have the potential to
provide the 'entire solution' to a given problem. However, these
tools should only be used by a suitably experienced modeller
to control the quality of the results and the interpretation of the
analysis. It should also be noted that there is an element of 'art'
to this type of modelling; hence it is unlikely that two different
engineers working on the same problem would get exactly the
same results. A 'suitable' modeller is an engineer who has suf-
ficient knowledge of the software, has sound experience or has
the support of experienced engineers who can review the results
both from ground behaviour and the structural response.
13.2.2.2 Spring models
This relatively simple form of analysis assumes that a structural
element is supported on or supporting (in the case of retain-
ing walls) a soil mass that is simulated as a series of springs.
This is often described as the subgrade reaction method. The
soil stiffness characteristics are recreated by assigning each a
spring stiffness. The stiffnesses may be varied in plan below
a footing or raft if a 'mat' of springs is used or vertically if a
retaining wall is being modelled.
It should be noted that although this method can be used
to calculate forces within a structural element together with
associated displacements, it will not provide any predictions
of ground movements adjacent to a simulated foundation or
at ground level behind a retaining wall. For embedded retain-
ing walls there are established relationships that correlate the
deflected shape of the wall to the ground settlement profile
behind it as shown in
Figure 13.4
.
