Define Static and Dynamic Formula in Pile Foundation
Pile foundation is a type of deep foundation that consists of long, slender members that are driven into the ground or cast-in-situ to support the load of a structure. Pile foundation can be classified based on different criteria, such as function, material, installation method, etc. In this post, we will focus on one of the aspects of pile foundation design: how to estimate the load capacity of piles using static and dynamic formulae.
Static Formulae
Static formulae are based on the equilibrium of forces acting on a pile under an applied load. They consider the soil resistance along the shaft and at the base of the pile as functions of soil parameters such as unit weight, cohesion, friction angle, etc. Static formulae can be used for both bored and driven piles, but they require accurate knowledge of soil properties and pile geometry.
One example of a static formula is the Meyerhof's method , which gives the ultimate load capacity (`Q_u`) of a pile as:
`Q_u = A_b q_b N_q + A_s f_s N_s`
where `A_b` is the base area of the pile;
`q_b` is the average effective stress at the base;
`N_q` is a bearing capacity factor;
`A_s` is the surface area along the shaft;
`f_s` is the average unit skin friction along the shaft;
and `N_s` is an adhesion factor.
The values of `N_q` and `N_s` depend on the type and condition of soil, and can be obtained from empirical charts or tables.
Dynamic Formulae
Dynamic formulae are used for driven piles. They are based on the principle of conservation of energy during pile driving. They relate the hammer energy input to the work done by the pile resistance and the energy losses due to friction, elastic deformation, and radiation.
Dynamic formulae can provide a quick estimate of pile capacity without requiring extensive soil investigation, but they have some limitations such as:
- They assume that the soil resistance is constant during driving, which may not be true for some soils that exhibit time-dependent behavior (such as clay).
- They neglect the effect of soil setup or relaxation after driving, which may increase or decrease the pile capacity over time.
- They may not account for the influence of adjacent piles or soil layers on the pile-soil interaction.
One example of a dynamic formula is the Engineering News Record (ENR) formula , which gives the ultimate load capacity (`Q_u`) of a pile as:
`Q_u = \frac{2 W h}{S + 0.1 d}`
where `W` is the weight of hammer;
`h` is the height of fall;
`S` is the final set per blow (penetration)
and `d` is the diameter of pile.
The ENR formula assumes that 10% of hammer energy is lost due to elastic deformation and radiation,
and that 90% is used to overcome the total soil resistance (static plus viscous).
Conclusion
Static and dynamic formulae are two methods to estimate the load capacity of piles in pile foundation design. Static formulae are based on equilibrium analysis and require accurate soil parameters, while dynamic formulae are based on energy analysis and require hammer data. Both methods have advantages and disadvantages, and should be used with caution and verification by field tests or numerical models.
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