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.
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).
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.
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:
- 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.
- 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.
- 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.
- 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.