Estimation of Hydrostatic Force
A Review for Realistic Approach
Estimation of hydrostatic force on underground structures is one of the important
loads to be considered for detailed design, and play a major role on the overall
economy of the structure. Present practice of taking full hydrostatic pressure under
large rafts may lead to uneconomical design. Hence, realistic estimation of ground
water table, pressure due to hydrostatic head, and the force acting on the structures
is of significance. Combination of ground water table at finished ground level,
combined with other critical loads, say, severe / extreme earthquake may lead to
unrealistic forces, though such condition may not arise during the life of the structures.
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Buildings with basements are normally provided with raft foundation of adequate
thickness. When the basement itself is in multiple floors, depth of foundation will
be in the order of 6 to 10 meters. Typical example is, underground multi-level basement
parking for mega shopping complexes. Traditional design approach is to consider
hydrostatic uplift due to the ground water present at the site under normal conditions,
as observed during the entire year, with its variation to envelope the uncertainties
involved in estimating the depth of water table from natural ground level.
For important structures, some of the designers consider ground water up to finished ground level, to meet any kind
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of uncertainty, and make
the design conservative. However, there is no codal provision for such consideration,
and thus is solely depends on the designer’s prerogative.
Hydrostatic Pressure
The pressure under the raft solely depends on a couple of factors, viz, density
of the water, and depth of ground water table. Mathematically,
γ : density of water
h : depth of ground water table from natural ground level.
H: Total hydrostatic force
l & b : Length and width of the building in plan.
W : Total downward loads due to dead load, live load, other incidental loads
Thus, conventionally, the force is estimated as, H = γ * h * l * b ……………..
(1)
However, certain conservative assumptions lead to overestimation of hydrostatic
force, and thus making the design of the building or structure as uneconomical.
Firstly, the above equation (1) is valid, only when the structure is floating in
water, such as, floating restaurants in lakes, and only water is present all around
the structure below the free water surface. There will not be any support from the
bottom of the lake, to keep the structure in floating condition. In such a case,
entire self weight of the structure, live load and other loads due to any equipment,
or incidental loads are balanced, entirely by hydrostatic uplift. In other words,
H > W, which keeps the building in floating condition. All the rules of fluid
mechanics are valid in such case, and the assumptions thus are applicable in -Toto.
Design of Nuclear Power Plant Structures
Normal structures are founded on competent strata below ground, and after the structure
is fully constructed, the area around the building is backfilled. In such a condition,
the rules of fluid mechanics are not applicable, hence cannot be applied for soil
founding media to estimate the hydrostatic pressure, even under fully saturated
soil condition.
All the safety related structures of Nuclear Power Plant are analyzed and designed
for various normal, severe and extreme environmental loads and their possible load
combinations. The analysis and design is being carried out as per various applicable
codes, such as AERB, ASME etc.
Out of the considered load combinations for such detailed analysis and design, some
of the combination includes Safe Shutdown Earthquake (SSE) / Operating Basis Earthquake
(OBE) and Ground Water Table (GWT) at Finished Ground Level (FGL). This assumption
leads to full hydrostatic below the raft at founding level. This assumption is quite
conservative, thus penalizing the structures, specially the large rafts of various
safety related structures, viz., Nuclear Building, Control Building, Station Auxiliary
Buildings, Waste Management Plant, various safety related pump houses and electrical
houses. Rafts of these structures are founded at depth, varying from 5 to 12 meters
below FGL, and thus leading to a hydrostatic pressure of 5 to 12 ton/sq.m, acting
upwards, on the raft.
Design Conditions
When the structure is founded on rock, three of the design conditions need to be
considered to keep the structure in safe conditions. These are explained in detail
further.
a) When W >> H, i.e the total vertical downward weight is very large and there
is no risk of floatation of the building under any condition during its service
life.
b) When W and H are comparable, i.e., the balancing hydrostatic pressure is nearing
the vertical downward force, there could be a risk due to flotation, when W <=
H. In such case, theoretically, floatation should take place, and the vertical displacement
can be estimated by u = (H-W)/(l*b). At such displacement, the building should be
stable, and floating above a water layer of thickness ‘u’.
c) When soil is fully saturated: In such situation, the pore water pressure develop
in the voids of the soil, and due to the nature of incompressible nature of water
at this pressure, water present in the pores try to dissipate the pressure through
lateral movement through inter-connected pores, till the excess pore water pressure
reduces to zero.
d) However, in routine buildings, which are founded on soil, additional factors
of safety exist, due to a) friction between backfilled soil around basement walls,
b) resistance from soil wedge failure surface, due to uplift of building, and c)
contact pull out resistance between soil and PCC or PCC and Foundation mat. Considering
these forces for stability check, will enhance the available factor of safety and
keep the structure in safe condition.
Loose sands and cohesionless soils may have voids, whose volume depends on the gradation
of the soil, and in-situ void ratio below the foundation raft. With progressive
construction, the void ratio will decrease further from the virgin soil condition,
and over the time, consolidation takes place and settlement occurs.
Realistic Scenario
When the vertical downward force is more than the hydrostatic uplift force, the
difference of these two forces is resisted at the contact are of foundation mat
and sub-base strata. Even with adequate voids in the soils, the net area of soil
solids (gross area –void area) will share the vertical load.
In absence of in-situ void ratio values, a conservative estimate of void cross section
area (as a percentage of gross area of foundation) at the bottom of the foundation
may be taken for design calculations. Hydrostatic pressure due to water table will
act only on the area of voids, and thus reduces the uplift pressure significantly.
This force can be considered to act on the bottom of the raft for detailed structural
response calculations (in terms of shear force and bending moment in the base raft).
Modified Design Methodology
With the above realistic assumptions, structures and their foundations are subjected
to lesser forces due to hydrostatic forces. This will lead to economical design
of the foundation raft also. However, these assumptions need to be proved with adequate
experimental measurements, and supported by analytical calculations. Till such time,
present conservative methodology can be used for day to day design purpose.
Probabilistic Safety Assessment
Assuming ground water table (GWT) at ground level is a highly conservative assumption,
and hence to be used cautiously. Designers are at their liberty to use most probable
level of GWT in place of GWT at ground level. A detailed PSA can also be carried
out to assess the probability of exceedance of GWT level above the average GWT level,
based on the past history.
This can be projected for a return period of 500 to 1000 years, when the design
life is taken as 50 years. Thus, the return period is 10 to 20 times more than the
design life of the structures.
Case Study of Nuclear Power Plant
Conservatively, assuming that the site is fully flooded for a period of one day
in a year, due to extreme rains, on the sloping ground and storm water drainage
is not possible, and ground water table is at FGL, the probability of occurrence
of such extreme hydrological event being considered in the design is 2.7*E-3.
The probability of occurrence of SSE is once in 10,000 years, or around 2.7*E-7
per day. This earthquake may last about 30 to 40 seconds, with peak acceleration
occurring for about 4 to 5 seconds only. Thus the combined probability of occurrence
of SSE together with GWT at FGL works out to be 7.29*E-10.
The probability of occurrence of OBE is once in 100 years, or around 2.7*E-5. This
earthquake may last about 30 to 50 seconds, with peak acceleration occurring for
about 4 to 5 seconds only. Thus the combined probability of occurrence of OBE together
with GWT at FGL works out to be less than 0.729*E-7.
The peak ground motion occurs for about 4 to 5 seconds, thus generating loss of
contact of raft (which is limited to 33%) with the founding media for a very short
time of about a couple seconds. Ground water gushing into the wedge shaped gap of
1.0mm to 2.0mm for this 33% portion of the total area of raft, and thus generating
full hydrostatic pressure within this short time to destabilize by overturning or
floatation or loss of contact, seems to be unrealistic and highly conservative,
hence needs a re-look.
Combining two such extreme environmental events, i.e. GWT at FGL with SSE / OBE,
with very low probability of combined occurrence as indicated above, seems to be
quite unrealistic situation, particularly in the case of arid zones.
Design Solutions
Various design options are in practices by consulting engineers, based on the subsurface
geotechnical conditions, safety margins needed for the structure under consideration,
functional requirement, economy etc. Some of them are indicated below,
- Use of projection beyond the structure boundary. This will help
in taking the weight of soil backfill above this projection. The water pressure
is 1.0 t/sq.m per meter depth, whereas, the soil is in the range of 2.0 t/sq.m.
However, this has one disadvantage, as, the projection need to be designed for full
vertical shear force, and may prove uneconomical when the depth of foundation is
large.
- Use of mass concrete to mobilize self weight. This may, at best,
add additional 1.5 t./sq.m per meter of extra thickness of raft at the basement.
Economics need to be worked out carefully, before designing such additional thickness,
to ensure safety of structure against flotation under a hypothetical condition,
which may not be seen by the structure during its life time.
- Use of Rock Anchors. When the structural configuration is such,
that, additional thickness of raft cannot be provided, design of raft with rock-anchors
become mandatory. This may be uneconomical, considering the overall cost of the
scheme.
The holes drilled in the founding medium (rock) need
to be grouted appropriately to avoid ingress of water into the voids. In addition,
corrosion of rock anchor may become an issue, even after grouting the hole drilled
for the anchors, as the grouting operation is totally blind in the founding media,
and may not be 100% fool-proof.
Conclusions
Based on the above, the following conclusions can be drawn.
- Hydrostatic force estimation cannot be neglected for the detailed
design of underground structures, subjected to saturation / submergence condition
due to ground water table and / or external flooding (due to various reasons).
- Estimation of most probable ground water table level play a key
role in estimating the hydrostatic force on the underground portion of the structures.
- Considering ground water table at finished ground level appears
to an unrealistic assumption, and may lead to uneconomical design.
- Precise estimation of hydrostatic pressure and the uplift force
based on in-situ void ratio of founding medium may lead to realistic design.
- For the structures having fragmented or highly weathered rock
as founding medium, the full hydrostatic force may not get mobilizes, as there will
be only seepage pressure on certain portion of the raft.
- Various design solutions can be worked out based on the functional
and system requirements, economics and in-situ conditions of founding strata.
- Detailed experimental programmed will certainly help in estimating
the hydrostatic force in realistic manner, thus leading to economic designs.
Acknowledgements: Association of Consulting Civil Engineers
(I), Mangalore Centre A3C – 12: Awards, Convention & Consultants Colloquium
January 11-12, 2013, And Mangalore, India. Built Expressions were the official media
partners for the same.