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Why Buoyancy Forces Cannot Be Ignored

Jul 28, 2010

Archive - 2009-2010, Precast Inc. Magazine, Precast Magazines

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Forces are at Work Beneath the Feet that Must be Reckoned With Before

Designing an Underground Structure

By Claude Goguen, P.E., LEED AP and Ronald Thornton, P.E.

Everyone probably remembers the images of US Airways Flight 1549 drifting in the middle of

the Hudson River Jan. 15, 2009, while frightened passengers disembarked onto the wings.

The courageous actions of the pilots and flight crew were credited for saving the lives of all

on board. But it was a physical force that kept the airplane afloat – a force known as

buoyancy.

Buoyancy is also an important element of the annual National Concrete Canoe Competition

hosted by the American Society of Civil Engineers. More than 200 university teams compete

for America’s Cup of Civil Engineering. The University of Berkeley won the 22nd NCCC title

this past June.

In the case of Flight 1549, or if you’re building a concrete canoe, buoyancy is a good thing.

For those in the underground utility business, however, it can be a pain if it is not accounted

for in the design.

Buoyancy is defined as the tendency of a fluid to exert a supporting upward force on a body

placed in a fluid. The fluid can be a liquid, as in the case of a boat floating on a lake, or the

fluid can be a gas, as in a helium-filled balloon floating in the atmosphere. A simple example

of buoyancy can be seen when trying to push an empty water bottle downward in a sink full

of water. When applying a downward force to the water bottle from your hand, the water

bottle will stay suspended in place. But as soon as you remove your hand, the water bottle

will float to the surface. The buoyant force on the object determines whether or not the

object will sink or float.

Buoyancy wasn’t officially documented and conceptually grasped until Archimedes (287-212

B.C.) established the theory of flotation and defined the buoyancy principle. He realized that

submerged objects always displace fluid upward. Then with that observation, he concluded

that this force (buoyant) must be equal to the weight of the displaced fluid. Archimedes then

went on to state that a solid object would float if the density of the solid object were less

than the density of the fluid and vice versa. But what is the basic procedure to follow in

order to determine whether an underground concrete structure will resist buoyant forces?

It can be determined if an underground concrete structure will float or sink using basic

principles. Essentially a concrete structure will not float if the sum of the vertical downward

forces is greater than the vertical upward force. When applying this principle to a structure

below grade, it can be said that if the buoyant force (Fb) is greater than the mass of the

structure and the combined mass of soil surcharges and objects contained within the

structure, the structure will float.

Why is buoyancy an important factor in the design of an underground concrete structure?

The simple answer is that the buoyant forces created by water need to be resisted to

prevent the structure from floating or shifting upward.

Determining water table levels

When designing an underground precast concrete structure, it is necessary to know what

structure to make as well as its intended use. Typically contractors who need precast

structures will present precasters with details on what they need and give design

requirements and information on the underground conditions.

Not always, however, do they inform precasters about every detail, especially job site

conditions and problems in the construction area. Site and subsurface conditions are vital

pieces of information needed for the design calculations to optimize the performance of the

structure in the installed condition and to prevent flotation. So how does the design engineer

determine when there could be a potential problem with the jobsite conditions and with

flotation?

First, the design engineer should review and investigate the plans, specifications and soils

reports to gain more insight about the project and the underground conditions. After

obtaining the requirements and specifications for the structural design, the design engineer

should obtain extensive information on the soils and subsurface conditions. One of the first

factors that must be determined when analyzing an area in which the concrete structure will

be placed below grade is the water table, or groundwater level. Obtaining this information

will help the designers identify sites where flotation may or may not be a factor in the

design. How can one determine the water table level in the project area?

The design engineer should check the soils report to obtain more information on the area.

The soils report is typically the most reliable source of data, as it’s based on a study of the

jobsite conditions. If there isn’t a soils report, core drilling may be necessary. By core drilling

in the vicinity of the project, the depth of the water level from grade can be determined. It

should be noted that groundwater levels identified on drilling reports are only a snapshot in

time and may not account for seasonal variations. Another possible source of information

would be from local well drillers, who typically maintain records of water table levels.

After the water table level has been determined and it is known that there will most likely

not be a problem with buoyancy or flotation issues, the designer can focus on maximizing

the structure without the consideration of buoyant forces. In most cases, flotation will not be

a problem in areas of the country without groundwater (parts of Texas, Arizona and Nevada)

and where the groundwater is below the anticipated depth of the structure. The fact that the

buoyancy force exists presupposes that the water table at the site is at an elevation above

the lowest point of the installed structure. If your structure is to be placed above the

groundwater level (according to the sites’ water table), less concern is needed. On the other

hand, areas where flotation causes potential problems are typically at low elevation where

the water level is at grade (valleys, ocean shores) and in areas where groundwater is

present below grade at the time of installation (before soil has been compacted).

Be aware of seasonal and regional variations

The water table is the upper level of an underground surface in which the soil is saturated

with water. The water table fluctuates both with the seasons and from year to year because

it is affected by climatic variations and by the amount of precipitation used by vegetation. It

also is affected by excessive amounts of water withdrawn from wells or by recharging them

artificially. The design engineer should make certain to account for seasonal and regional

fluctuations in the water table level in the design of an underground precast concrete

structure; this will ensure that the underground structure will not float or shift upward from a

water table level miscalculation.

Err on the conservative side

If there are no soils reports or previous water table data available for fluctuations (seasonal

and regional), most engineers will design the structure on the conservative side. This will

ensure that the structure will be able to withstand seasonal and regional fluctuations.

Designing on the conservative side refers to a structure with the water level at grade, even

if flooding in that area is not common. A conservative design pproach may contribute to

offsetting unnecessary and unforeseen costs when sufficient information about the soil/site

conditions is unavailable. Therefore, overdesigning a structure should be kept to a minimum

since this would add substantial costs to production.

Computing downward (gravity) forces

After the water table level has been identified, the design engineer needs to look at

computing all the downward forces that will be acting on the structure. All vertical downward

forces are caused by gravitational effects, which need to be calculated in the design of an

underground structure. Essentially, the engineer determines if the total downward forces

(gravitational, WT) are greater than the upward force (buoyant, Fb). The total downward

force (WT) is calculated by the summation of all downward vertical forces (W).

Depending on the design of the underground structure, the total vertical downward forces

(WT) may or may not be the same for all applications. In a conservative approach, the

design of underground structures assumes that the water table at the specific site is at

grade. In this case, it is essential to account for all vertical downward forces (WT) to ensure

that the structure will not float (WT > Fb). For an underground structure, designed for a

worst-case scenario, the following vertical downward forces (W) need to be considered:

Weight of all walls and slabs

Weight of soil on slabs

Weight of soil on shelf or shelves

Weight of equipment (permanent) inside structure

Weight of inverts inside structure

Friction of soil to soil

Additional concrete added inside structure

Weight of reinforcing steel

As noted previously, not all underground structures are the same, and therefore some of the

listed vertical downward forces (W) above may not be included in the summation of total

vertical downward force (WT).

Computing upward buoyant force

As stated in Archimedes’ Principle, an object is buoyed up by a force equal to the weight of

the fluid displaced. Mathematically, the principle is defined by the equation:

Fb = gf x nd

Fb = buoyant force (lb)

gf = density of water (62.4 lb/ft³)

nd = displaced volume of the fluid (ft³)

When analyzing buoyancy-related concrete applications, the structure is typically below

grade and stationary. Assuming the application is stationary in a fluid, analysis uses the

static equilibrium equation in the vertical direction, S Fv = 0. Analyzing buoyancy related to

underground structures requires use of the same static equilibrium equation, assuming the

structure to be stationary and either submerged or partially submerged in a fluid (in the

latter case, the surrounding soil /fill material and any associated groundwater).

Safety factor guidelines

The Factor of Safety (FS) considers the relationship between a resisting force and a

disturbing force. In this case, it’s the relationship between the weight of the structure and

the uplift force caused by buoyancy. Failure occurs when that factor of safety is less than

1.0.

Generally speaking, the greater the FS the greater the impact to the project/structure. An

optimal design would be an appropriate FS that is adequate for the conditions present at

that specific site. It is recommended that the designer choose an appropriate FS after

reviewing jobsite information.

According to ACI 350, the safety factor against flotation is usually computed as the total

dead weight of the structure divided by the total hydrostatic uplift force. The FS should

reflect the risk associated with hydrostatic loading conditions.

In situations of flooding to the top of the structure and using dead-weight resistance only, a

FS of 1.10 is commonly used. In flood zone areas, or where high groundwater conditions

exist, a FS of 1.25 can be used. Where maximum groundwater or flood levels are not well

defined or where soil friction is included in the flotation resistance, higher FS values should

be considered.

Buoyancy countermeasures

There are several methods that can be used in the industry to overcome a buoyancy

problem. If the design of the underground structure does not meet the required safety

factor, there are ways to fix the problem. Here are some different methods used to

overcome buoyancy, both before and after shifting or flotation:

1. Base extension (cast-in-place or precast). Using the additional weight of soil by

adding shelves is a common method used to counteract buoyancy. Extending the

bottom slab horizontally creates a shelf outside the walls of the structure and adds

additional resistance to the buoyant force. The additional vertical downward force

comes from the additional weight of the soil acting on the shelves (Wshelf). The size

of the shelf can be designed as large and wide as needed so the buoyant force is

resisted. However, limits in shipping width must be considered. In many cases, this is

the most cost-effective method used to resist the buoyant force (Fb). When pouring

the shelf in place, mechanical connections must be designed to resist the vertical

shear forces. If possible, it is best to have the shelf monolithically poured with the

structure.

2. Anti-flotation slab. Another method that has been used in construction is to anchor

the structure to a large concrete mass (shelf) poured on site or use precast concrete

manufactured off site. The structure sits directly on top of this large concrete mass

that has previously been poured in place or cast, cured and delivered by an off-site

manufacturer. This method can cause problems, however, because both base slabs

must sit flush on top of one other. If base slabs are not aligned perfectly, cracking

due to point loads may result. Cast-in-place concrete can be expensive and cause

delays due to strength curing time. Precast concrete alleviates alignment and delays

for strength gain, but the sub-base must be level and set flush. A mortar bed

between the two surfaces is recommended. To design the mechanical connection

between the anti-flotation slab and the structure, the net upward force must be

calculated. This calculation can be achieved by multiplying the buoyant force by the

FS, and subtracting the downward force.

3. Increase member thickness. One method used to overcome buoyancy is to increase

the concrete mass (m). This is accomplished by increasing member thickness (walls

and slabs). Increasing the thickness of the walls and slabs can add a significant

downward gravitational force, but this may not be cost effective. Increasing concrete

mass can be an expensive alternative due to increased materials and production

costs.

4. Lower structure elevation and fill with additional concrete. Another method used to

overcome buoyancy is to set the precast structure deeper than required for its

functional purposes. This will add additional soil weight on top of the structure to

oppose buoyant forces. Also, with the structure being deeper in the soil, some

contractors opt to pour additional concrete into the base of the installed precast

concrete structure. This will add more mass to the structure, which helps overcome

buoyancy (m > Fb).

It is a fairly simple concept: downward gravitational forces need to exceed upward buoyant

forces. Ignoring this may result in your structure surfacing like a submarine in the South

Pacific. Once a precast vault is installed underground, you expect it to stay put. Since

concrete is about 2.5 times heavier than water, one would not expect flotation to be much of

an issue with buried concrete structures, but in fact it is a serious consideration in areas of

high ground water.

Claude Goguen, P.E., LEED AP, is NPCA’s director of Technical Services.

Ronald Thornton, P.E., is a project manager for Delta Engineers in Binghamton, N.Y., with

more than 25 years of experience in the concrete industry. He has extensive experience in

the design, manufacture and installation of precast products for use in state, municipal and

private projects. Thornton currently serves on the NPCA Utility Product Committee as well as

the ASTM C27 Committee.

This article was originally published in the September-October 2009 issue of Precast Inc. You

can view all the issue’s articles here on this website, or you can view the full print

publication by clicking the cover above.

 

 

 

Tags: buoyancy, underground structure

ONE COMMENT ON “WHY BUOYANCY FORCES CANNOT BE IGNORED”

1. Bob Grotke on June 13, 2012 at 3:29 pm said:

The problem of bouyancy became an issue at my workplace a while back. Our department

has used open bottom fiberglass manholes for years and the typical installation involved

dewatering the excavation as required, placing the fiberglass manhole in the proper

orientation for the sewer pipes, and pouring mass concrete around the base of the manhole,

typically at least 1 foot thick and 1 foot wider than the manhole diameter all around. After

an initial set, the excavation would be backfilled and compacted while the dewatering

system remained operating. The interior base of the manhole would be finished with

additional concrete, formed to provide a flow channel with built up concrete haunches to

direct the flow. After construction was complete, the dewatering system would be removed

and the ground water would return to seek its own level. Design was typically conservative

with satuarated ground assumed up to finished grade. We had never had any problems with

this construction, but the engineers managing the office one day decided that a 2-way

reinforcing steel mat was required in the concrete base to resist “unopposed hydrostatic

forces” that could cause the cured concrete to fail. I was assigned to determine what

reinforcement was necessary. I stated that none was necessary as the weight of the

manhole, concrete base, manhole lid and frame and the soil surcharge overcame the

bouyant forces, the net force was downward and any resulting bending stress in the

concrete was within the limits allowed by the ACI “plain” concrete building code. This

resulted in much heated discussion and agravation. I finally told management that if they

sincerely believed the reinforcement was necessary, they should just direct the crews to

install the reinforcement and they wouldn’t get any arguments, however I believed it was

not necessary. The bad feelings resulting from this situation eventually led me to find

emplyment elsewhere, but to this day I wonder if their thoughts about “unopposed

hydrostatic forces” had any merit.

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