| Slurry walls offer several advantages over conventional retaining
wall design, particularly in congested urban areas, in that they
can:
- Resist lateral earth and water pressures and earthquake forces
- Behave as load-bearing elements
- Serve as the temporary as well as the permanent structural
wall for a tunnel or underground building, providing a finished
concrete surface.
Fundamentals of Slurry Wall Design
Design of a slurry wall is greatly dependent on the method of analysis
used and requires close communication between structural and geotechnical
engineers. The three primary analysis methods are:
- Equivalent Beam on Rigid Support (Rigid Method).
The point of zero pressure is computed below the excavation cut
(passive pressure set equal to active pressure), and acts as a
fictitious support. As excavation proceeds, the wall spans as
an elastic beam between rigid supports (provided by bracing members
or floor slabs) with the lowest support at the point of zero pressure
below the subgrade. This method may be conservative, but provides
an easy structural solution. The computed wall deflections from
the elastic analysis do not, however, correlate to predicted ground
movements.
- Beam on Elastic Foundation (Winkler Method).
The passive side of the wall is modeled as a series of “springs”
based on the modulus of subgrade reaction of the soil. The elastic
properties of the soil are required in order to calculate the
soil modulus. Analysis is carried out with general structural
computer software to determine moments and shears. This method
allows complete modeling of the wall based on soil springs, brace
or floor springs (K-values based on stiffness and volume change).
It seems to yield smaller forces than the Rigid Method and also
gives a better indication of wall movement. Given the various
unknowns inherent in soil properties, actual versus assumed loads,
and other such factors, a cautious elastic approach to analysis
should be exercised.
- Finite Element Method (FEM). This method requires
advanced computer software and modeling, and an in-depth knowledge
of soil properties that are modeled in the program and construction
sequences that are simulated. Its greatest benefit is better prediction
of soil movement. Its use for structural design is limited and
reliance on other methods is necessary.
I suggest using these three methods as follows:
- The Rigid Method merits consideration as a
first choice or as a preliminary tool due to its simplicity.
- The Winkler Method offers an attractive solution
in that it gives a more realistic representation of wall behavior.
It could be used next as a check or for design. Then, engineering
judgment should be used on a case by case basis taking into account
the degree of conservatism desired.
- FEM is a powerful tool that enables designers
to analyze many construction stages and temporary excavation
conditions. Its use is recommended as a supplement and where adjacent
construction may be sensitive to wall movements and a better prediction
of these is required.
Regardless of the method used, it is essential that close coordination
and communication take place between geo-technical and structural
engineers early in the design process, and a consensus and understanding
be reached. This must be followed by coordination meetings with
the contractor to minimize problems during construction.
Slurry Wall Penetration
The depth of wall penetration below subgrade or dredge level is
governed typically by stability although water cutoff and bearing
must also be considered. The forces pushing into the excavation
must be balanced by resistance provided by the subgrade penetration
and bracing. In most cases, the design depth is controlled by the
loading case in which excavation is at its final stage, just before
installation of the lowest slab or bracing member. For this calculation,
it is typically assumed that the wall below this level does not
contribute its own stiffness. Because the wall is free to rotate
about its lower end, a safety factor with respect to passive resistance
must be used in the design. A value of 1.5 is recommended typically.
Figure 1: Slurry Wall Penetration |
The required penetration (d) is determined by equating to zero
the sum of the moments on the active side and passive side about
the brace point or floor level above (Figure 1). This condition
yields a cubic equation in which d is easily solved by substituting
trial values. The embedment is often arbitrarily increased by 20
percent.
Some engineers may want to take advantage of the additional bending
resistance provided by the wall at the brace elevation and/or the
moment capacity of the brace point at the connection to the wall.
This is an engineering judgment that should be used on a case by
case basis, depending on the degree of protection provided by other
systems utilized, and several factors including overall degree of
conservatism in selection of soil parameters, method of analysis,
accuracy of loads and ground water pressure, existing adjacent foundations,
etc. The same rationale should also be used in determining the magnitude
and applicability of safety factors that must be incorporated in
the design.
Another interesting calculation to perform is to consider the effect
of base friction on the wall penetration, taking into account the
coefficient of friction between concrete and the rock or bearing
material. Here, too, an engineering judgment must be made as to
whether or not to rely on this information.
A Case Study: North Station Parking Garage
Boston’s North Station Underground Garage illustrates some
of the current methodology used in the design of slurry walls. The
construction of this 6-level underground structure was at the site
of the new Shawmut (now Fleet) Center sports arena. It included
0.9-m (3-foot) thick reinforced concrete slurry walls 18 to 24 m
(60 to 80 feet) deep, embedded in bedrock. The wall panels vary
in length from 2.6 to 7.6 m (8.5 to 25 feet). The “top-down”
method of construction was selected because of the large footprint
area of the garage, the scheduled arena construction above, and
the extremely tight physical constraints of the site, which was
surrounded by the existing Boston Garden, the underground Orange
Line subway tunnel, the Federal Administration Building (GSA), and
the Central Artery Ramp structure.
First, the slurry walls were built around the site. These walls
acted as horizontal water cut-off and also became the permanent
wall of the structure. Interior steel columns were installed from
grade in a slurry trench technique (filled with tremie concrete
at the base) to form supporting caissons. The ground floor level
was then built around the columns, which support it. The completed
slab braced the slurry wall while the garage was mined below it.
The ground floor slab braced the excavation, eliminating the need
for conventional internal bracing or tiebacks. This step was repeated
for the lower levels.
When designing the slurry wall, we analyzed it for all stages of
construction because it was to be both a temporary and permanent
excavation support element.
- During Construction. Active lateral pressures
were assumed and a triangular pressure distribution was used.
The passive pressure was computed at various excavation levels
and the point of “zero pressure” was used to compute
the reaction below excavation level (Rigid Method). This was checked
later using the Winkler Method. A finite element analysis was
also performed, and the wall analyzed based on predicted slurry
wall deformations. The calculated bending moments were lower than
the ones obtained from the other analyses.
- End of Construction. Prior to casting the
lowest base slab (six levels down), active lateral pressures were
assumed, but based on a rectangular distribution. The pressures
were used to determine slurry wall penetration and stability,
which was obtained by equating to zero the active and passive
moments about the level above.
- Long Term (Permanent Loading). At rest, lateral
pressures (triangular distribution) were used for the long-term
design of the slurry wall
Figure 2: Reinforced Slurry Wall Section |
Figure 3: A section of the stirrup reinforcing detail. |
The slurry wall was designed for soil, groundwater and surcharge
pressures in all three stages, and for seismic pressures in the
long-term stage. A safety factor of 1.5 was applied to passive soil
pressures. To obtain a comprehensive bending moment envelope along
the height of the wall, the support reactions provided by the floor
slabs at each stage were considered “rigid supports”
(zero deformation) as well as “flexible springs,” taking
into account the elastic shortening of the slab and volume change
deformations resulting from creep, shrinkage, and temperature variations.
During construction, an extensive monitoring program was performed
that included observation wells, inclinometers, and settlement measurements.
This program was necessary to verify that wall movements were similar
to those assumed during design.
Theory Versus Practice
What does all this mean to structural design? Engineers often fall
back to the ACI 318 concrete building code and design a slurry wall
for flexuq`re and shear that are the same as for walls cast above
ground. There is a major difference, however, in that slurry walls
are constructed somewhat “in the blind” without the
convenience inherent with exposed construction as far as placing
and curing concrete, controlling form dimensions, and placing reinforcement.
For these reasons, a moreconservative approach to design and detailing
is warranted, including making allowances for anticipated construction
tolerances and keeping in mind that the finished product is not
as shown by the neat straight lines on the contract drawings (Figure
2).
Some specifics of flexural and shear design are shown in the accompanying
box. Crack control and wall/soil deflection/ displacement must also
be considered, however, in a typical design.
Conclusion
In summary, flexural and shear design for slurry walls must take
into account not only the structural integrity and code requirements,
but also:
- The detailing of the contract documents
- Construction practices in the area
- The increased tolerances associated with this type of construction.
The recommendations presented in this article are intended to
facilitate structural design, bring awareness to the differences
between design and construction, and provide a more durable concrete
wall that will exhibit fewer cracks and leaks and help reduce the
long-term maintenance that may be required.
As structural engineers, we must acknowledge that the ultimate performance
of the slurry wall is more significantly affected by construction
techniques and site-specific subsurface conditions than it is by
the structural details and code interpretations. |
