I have been doing finite element analysis using Matlab. I look for many examples and tutorials producing only the stiffness matrix letting elements being weightless. However, in my case, I need to do a soil deformation where the self-weight of elements is significant.
Any guidance will be appreciated.
A load due to gravity or self-wieght is commonly referred to as a body force in continuum mechanics. Finite element texts often use this term when referring to this type of loading.
For each finite element, an equivalent nodal force vector due to body forces can be calculated as
$$ {\bf f}^e_i = \int N_i \left\{ \begin{array}{c} b_x \\ b_y \end{array} \right\} dV $$
where $N_i$ is the element shape function at the ith node, $b_x$ the body force in the x direction, and $b_y$ is the body force in the y direction. For a gravity load in the negative y direction, $b_y = -\rho g$ where $g$ is the acceleration due to gravity and $\rho$ is the material density.
The element ${\bf f}^e_i$ are assembled into the global load vector in a manner analogous to how element stiffness matrices are assembled.
If you want to learn more, most finite element texts that emphasize structural analysis discuss this procedure in sections describing calculation of equivalent nodal loads. For example, see section 4.2 in http://www.amazon.com/Finite-Element-Procedures-K-J-Bathe/dp/097900490X
