Environmental Engineering Reference
In-Depth Information
(c)
Inclusion of water pressure loads and internal pore pressures
Most finite element analysis programs are geared up to cope with internal pore pres-
sures so generally engineers have opted to apply the reservoir water loads to the dam's
upstream face and any exposed dam faces of cracks. The final effective stresses within
the body of the dam are found by adding the pore pressures to the calculated stresses
from the FEM analysis (compressive stresses usually taken as negative). Some engi-
neers apply the water load to the dam's face and uplift as an external load to the base.
This approach does not allow the correct results to be achieved in a step-by-step
numerical integration procedure. To overcome this shortcoming, analyses can be done
to define the seepage pressure forces. Typically, for an FEM package that has a heat
flow model contained within it, this heat flow program, with assumed boundary con-
ditions (for example, the very conservative assumption of full head at upstream face
and zero at downstream face), can be used to calculate these seepage forces. In effect,
the total water pressure loads are included as body forces in much the same way as
gravity forces.
If the stress distribution is required within the foundations, then similar body force
distribution can be found. The pre-existing groundwater conditions need to be
included - for example the original grand water surface could be assumed as coinci-
dent with the ground surface (probably appropriate to a dam section near or at max-
imum section).
The pore pressures are usually assumed not to change during the earthquake. Some
have argued that this assumption should not apply to a crack that opens and closes
cyclically, but most design guidelines recommend that the “unchanged” pore pressure
model is acceptable.
(d)
Shear strength conditions at crack elements
Ideally, the chosen shear strength law should have peak strength used until shear dis-
placement starts at which point the strength would drop to the appropriate residual
strength law. The residual strength would apply thereafter. One would have to nomi-
nate a complete shear failure path, usually a planar surface on the section or at the
dam-foundation interface. Movement would not be assumed until all crack elements
on that surface have reached the peak strength.
This relatively complex model, as far as the authors know, may not be readily avail-
able in FEM packages. Accordingly, the procedure is usually to adopt the residual
strength as the shear strength law from the start of the analysis. The calculated perma-
nent shear displacement for most analyses would therefore tend to over-estimate the
shear displacement on any selected surface.
(e)
Damping
Damping, usually as a percentage of critical damping is an important input for any
FEM analysis. Some practising engineers choose the damping factor at the low value,
say, 5% of critical damping, arguing that the dam's stress levels are relatively low so
damping will be correspondingly low. Others argue that any crack development, per-
manent shear displacement, the presence of defined contraction joints between blocks
and similar features warrant selection of a damping factor approaching 10-12%, par-
ticularly for MDEs with a pga above 0.3 g. The authors favour the selection of damp-
ing factors close to 10% for an MDE analysis. Strictly, damping should be varied
throughout the analysis, but the simple approach of a constant factor is generally
applied from the start.
16.9.3.6
Design earthquake input motion
Regardless of whether the response spectrum or the accelerogram (acceleration time-
history) input is the basis for the analyses, several selected sets of input data should be
used. Advice should be sought from a specialist seismologist on this input data.
