Because soils are in general complex materials that consist of the soil skeleton, the pore air, and pore water and exhibit non-linear stress–strain behaviour and perhaps time-dependent behaviour, it is not always simple to obtain analytic solutions to problems. Analytic solutions are those that contain closed form solutions that may be a simple algebraic formula that can be evaluated. Some solutions are semi-analytic, for example, the solution may be written as an integral that is not able to be inverted through analytic means and has to be evaluated using numerical integration. Finally, there are the numerical solutions that rely on numerical approximation rather than algebraic manipulation for their solution.