foundation system of burj al arab

What is the Significance of Modulus of Subgrade Reaction of Soil?

Modulus of subgrade reaction is an important term that is frequently used in structural analysis of components of foundation. This is used to design continuous footings, rafts and different types of piles. Modulus of subgrade reaction is a relationship between pressure and associated deflection of soil. Plate load test can produce these data. A δ Vs σ plot is produced during testing; the plot is found non-linear in most cases. Whether tangent or secant lines are used to determine slope (i.e. Ks). The basic equation is
Modulus of subgrade reaction-1


Δσ=increment of soil pressure 
Δδ=respective change in deformation or settlement

Tangent line is shown as solid line and secant line is shown as dashed in the following figure. Generally, initial line passing through origin is used, but tangent at any point or average of two values taken at the points intersected by scant line drawn along the curve can be used.

Except significantly small plates, it is very difficult to conduct plate load test as reaction load is necessary to achieve uniform deflection of plate. Even in case of small plates like diameter of (450~750) mm, it is not possible to derive δ conforming definition of Ks as plates shown tendency to be too rigid to produce constant deflection along the plate dimension. The rigidity can be increased to some extent by staking smaller plates placed concentric with underneath larger one, whatever measures are taken, the plot is done with load applied on load block derived by contact area (i.e. nominal value q =P/A) and average value of measured deflection.

Following figure describes the situation, figure 1 shows two region of q Vs δ plot where Ks is considered constant up to average deflection value Xmax. When deflection exceeds Xmax, the soil pressure is taken as constant as defined by

qcon = Ks (Xmax)

one can split q- δ plot into several potions so that modulus of subgrade reaction (Ks) attains it actual values on the slope

Factor Controlling Workability of Concrete

Concrete in fresh state is moldable mix which can be placed with reasonable amount of compaction and finished with selected means. The two qualifying words (adjective), reasonable and selected are actually refer to workability. A concrete is said to be workable when internal and external friction can be overcome with reasonable amount of effort exerted by compaction which indicates ease in placing, compaction and finishing as well. The factors that control workability or in simple word that offers lubrication effect on fresh concrete by reducing friction to ensure easy compaction are as below:

• Water content
• Aggregate size
• Aggregate shape and their surface texture
• Grading of aggregate
• Application of admixture
• Mix proportions

Besides these we can explain influencing factors on workability based on only three terms

• Water/cement ratio
• Aggregate/cement ratio
• Water content

Some can also include external factor like temperature, air flow etc. Again cement content and aggregate grinding has also influence on initial workability and change in workability of mix.

Water content:

Water content in fresh concrete has significant influence on workability of concrete. This is the main factor that defines fluidity of concrete, the higher the value for a given volume of concrete , the higher the fluidity of concrete (expressed as kg (or liters) per cubic meter of fresh concrete). As it is often misunderstood fluidity as workability, an inexperienced supervision frequently depends on inclusion of more water in concrete to improve workability.

This practice becomes very common as it is the one of the simplest way that can be adopted at site. It should be noted that addition of water is the last option to improve workability of concrete (applicable even to uncontrolled concrete). In case of controlled concrete, arbitrary increase in water content is not permitted. To keep water/cement ration of the mix unchanged with the addition of water, cement content also have to be increased to meet the design strength of hardened concrete.

Aggregate size:

A large size of aggregate will offer least amount of surface area for given volume of concrete. Thus the surface area available to be wetted by water will be less, again less amount of paste or matrix will be required to lubricate surface of aggregate. Thus less matrix and less amount of water is required to overcome internal friction between particles. For particular amount of water and paste, larger size of aggregate will offer higher workability, but within some limit.

Aggregate shape and their surface texture:

Shape of aggregates has good influence on workability. Flaky or elongated and angular aggregate make mix very harsh as compared to cubical or round shape aggregate. Rounded shaped aggregates contribute better than others, as for a given volume (or weight) such aggregate will have least surface area then flaky or angular aggregate. They also can be packed with least voids and by nature a round shape particles exert least frictional resistance. This is why sand and gravel collected from river bed offer greater workability them sand and aggregate derived from crushed stone.

Very low water/cement ratio is essential in production of high performance and high strength concrete. When water/cement ratio as low as 0.25, all the factors, may be minor, has to be taken into account and in that case shape of aggregate is a vital factor in present construction industry. It should be remembered that natural source of sand will be exhausted very soon or become very costly and there will be no choice to choose manufactured sand. The shape of sand from crushed source is not very useful in respect of workability but now some modern crushers are available that can produce well graded and well-shaped aggregates. . The shape of sand from crushed source is not very useful in respect of workability but now some modern crushers are available that can produce well graded and well-shaped aggregates.

When surface texture of aggregate is concern, it has also influence on workability by again considering surface area available to receive and get wetted by water. Having same size and shape of aggregate, a rough textured aggregate need more water and paste than a smooth textured aggregate. Thus rough textured aggregate in concrete mix will produce a less workable concrete than that have glassy or smooth textured aggregate. Not only the water demand play roles in defining workability but also to some extent low friction between aggregate particles offer higher workability.

Grading of aggregate:

Grading has significant, can be said maximum, influence on concrete workability. Well graded aggregate means all sizes of aggregates remain in the mix which will render compact packing of mix