a$)$ Explain the preferance to use empirical correlations, based on the results of pile loading tests and dynamic or static penetration tests, to estimate the values of $\backslash ($ q b $\backslash )$ and $\backslash (\backslash$mathrm$\{$q$\}^\{\backslash$mathrm$\{$s$\}\}\backslash )$ in pile foundation design.

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b$)$ A precast concrete pile $\backslash (500\backslash$times $500\backslash$mathrm$\{$~mm$\}\backslash )$ in section is to be driven into a riverbed, which consists of a depth of sand. The results of standard penetration tests in the sand are as follows:

The pile is required to support a design compressive load of $800$ kN and to withstand a design uplift load of $200$ kN $.$ Determine the depth $($ Db$\backslash ()\backslash )$ to which the pile must be driven

i$.$ according to the traditional method with an overall load factor of $2\mathrm{.}0$ and

ii$.$ According to the limit state method.