Prevailing assumptions about slab design may not hold water.
By Gary K. Munkelt, P.E.
This technical article is the first of two in Precast Solutions magazine to discuss the effects of groundwater and floodwater pressure on the design of bottom slabs of precast concrete structures buried in the ground.
In some parts of the country, the design of precast concrete structures placed underground includes the assumption that water level in the ground could be at grade or, in flood-prone areas, above grade. The structure presented here is for instances where precast units are submerged in water. In cases where the structure is submerged in groundwater, some engineers erroneously assume that the bottom slab must be designed to withstand water pressure in addition to dead loads of the structure; this technical article is intended to clarify this mistaken assumption.
Four different design conditions for underground precast structures
Condition 1. Precast structure during installation: A clear understanding of loads applied to the bottom slab when water level in the ground is below the structure will benefit the designer. Consider the structure during installation when it is first placed in the excavation (see Figure 1).
Where:
Pv = vault pressure on the soil in psf
Wv = weight of the precast vault in pounds
Abs = area of the bottom slab in contact with the soil in
square feet
psf = pounds per square foot
The weight of the walls and top slab of the vault (Wv) in pounds divided by the area (Abs), in square feet, in contact with the soil yields a vault pressure on the soil of:
Condition 2. Precast structure after backfilling: When backfill occurs on a structure buried below grade (see Figure 2), the weight of soil will add to the design load of the bottom slab. In this case, water level in the ground is below the structure.
Where:
pe = pressure on soil in psf
We (dry) = weight of dry earth above vault in pounds The weight of the dry soil, or earth (We (dry)), in pounds, divided by the area of the bottom slab (Abs) in contact with the soil yields a pressure on the soil of:
Condition 3. Precast structure under live load: Normally, the design must include an allowance for a live load (LL) at the surface. This live load is usually a truck wheel load (in pounds) that is dispersed through the soil over an area larger than the footprint of the wheel at grade. Force due to live load (pLL) is a function of the wheel load, the footprint of the wheel on the pavement and the depth of the soil above the precast vault (h2) (see Figure 3).
Where:
LL = live load in pounds
pLL = live load pressure in psf
ALL = area of live load on top of vault in square feet
a = the length of the footprint at grade at the top of the pressure trapezoid
b = the width of the footprint at grade at the top of the pressure trapezoid
h2 = height of soil above the precast structure in feet
The dimensions in feet at the bottom of the pressure trapezoid are given as: a + 1.75 h2 and b + 1.75 h2 (see Figure 4).
Codes vary on interpretation of the “Area” of live load
(ALL) pressure at the top slab. A common method used by highway engineers is:
The live load in the previous equation, pLL, can be added to the dead load of the vault (pv) and weight of dry earth (pv) to arrive at pressure from the vault in the design load of the dry earth (ps) when water is not present in the ground, as follows:
Where:
ps = design pressure load in psf
pv = pressure of the precast vault in psf
Condition 4. Precast structure in saturated soil: The effect of water in the ground, or a saturated soil condition, needs to be considered. We need to remember a concept from physics that states: “A body submerged in water is buoyed up by a force equal to the weight of the water dispersed.” Thus, a body weighs less when in water than when it is on dry ground. This concept applies to the weight of the precast structure and the weight of soil above the structure; it does not affect live loads (LL) at grade.
Apply the physics principle to the formulas derived for dry conditions and assume the water level in the ground has risen to grade. Since forces from live load (LL) do not change, pLL will be the same for both dry and saturated conditions. The weight of earth (We (dry)) and the weight of the structure (Wv) will be affected by the buoyant force of water (see Figure 5).
Where:
We (sat.) = weight of the saturated earth above the vault in pounds
Wv = weight of the precast vault in pounds
We (dry) = weight of dry earth above the vault in pounds
pcf = pounds per cubic foot
Wv (in water) = weight of the precast vault in saturated soil
h1 = height of soil adjacent to the precast structure in feet
h2 = height of soil above the precast structure in feet
62.4 pounds = weight of one cubic foot of water
pwater = pressure of water on bottom slab in psf
In water, the weight of soil, or saturated earth (W e (sat.)), becomes:
And weight of vault becomes:
Now add pressure of water on bottom slab, where:
pwater = pressure of water in the ground in psf
And:
Substituting for We (sat) and Wv (in water), the equation becomes:
This equation reduces to:
This formula is the same as the design load calculated when water is not present in the ground. It can be concluded that the design load (ps) on the bottom slab is the same for dry conditions and for conditions where water levels in the ground are at or below grade.
The next issue of Precast Solutions will discuss loads applied to underground precast structures during flood conditions where water is above grade.
Gary Munkelt is a consulting engineer with Gary K. Munkelt & Associates in North Wales, Pa. Contact him at [email protected].
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