Intro Doc
$\underline{Introduction}$ $\\$ Settlement of shallow foundations include both the elastic settlement, consolidation method, and secondary method. For sand and stiff and overconsolidated clay, the elastic settlement is the primary component and can be predicted using the elastic theory, Janbu's method, Mayne and Poulos's method, and Schmertmann's method. Consolidation settlement is the predominant settlement component in soft clays. Primary settlement needs to be considered for plastic soils. $\\$ $\\$ $\underline{Janbu\space Method}$ $\\$ This method is applicable to the prediction of elastic settlement of stiff and overconsolidated clay. For these soils, the Poisson's ration, $\nu$, is assumed to be 0.5. \begin{equation}\label{eq3} \delta=A_1 A_2 \frac{PB}{E}(1-\nu^2) \end{equation} where $A_1$ is the influence factor for the foundation shape and compressible layer thickness and $A_2$ is the influence factor for the embedment depth (see Fig. 7.1 in Das' book); and E is the Young's modulus. These two factors can be calculated using the following equation: \begin{equation}\label{eq3a} A_1=f\left( \frac{H}{B} , \frac{L}{B} \right) \end{equation} \begin{equation}\label{eq3b} A_2=f\left( \frac{D}{B} \right) \end{equation} Young's modulus can be calculated in different ways, for example \begin{equation}\label{eq4a} E=\beta \cdot C_\mathrm{u} \end{equation} \begin{equation}\label{eq4b} E=E_\mathrm{s} \end{equation} where $C_\mathrm{u}$ is the undrained modulus and $E_\mathrm{s}$ is the equivalent modulus. $\beta$ can be calculated using Eq. 7.2 in Das' book and $E_\mathrm{s}$ can be calculated using Eqs. 7.25-7.27 in Das' book.