Theory

This section presents the theoretical foundations on which the program is based. Explain the concepts, assumptions, and formulations used in the different analysis methods implemented.

The content is intended to provide a clear understanding of how the calculation is performed within the software, facilitating both the interpretation of the results and the technical validation of the models.

Rankine active earth pressure

The following equation is used:

P_a=\frac{1}{2}\gamma H^2 K_a

Where:

$P_a$ : Active earth pressure ( $\text{kN}$ ).
$\gamma$ : Unit weight of soil ( $\text{kN/m}^3$ ).
$H$ : Wall height ( $\text{m}$ ).
$K_a$ : Coefficient of active earth pressure, which depends on the angle of internal friction of the soil and the angle of inclination of the wall face (dimensionless).

With $K_a$ defined as:

K_a = \tan^2 \left( 45° - \frac{\phi'}{2} \right)

Rankine passive earth pressure

The following equation is used:

P_p=\frac{1}{2}\gamma D_f^2 K_p

Where:

$P_p$ : Passive earth pressure ( $\text{kN}$ ).
$\gamma$ : Unit weight of soil ( $\text{kN/m}^3$ ).
$D_f$ : Depth of foundation ( $\text{m}$ ).
$K_p$ : Coefficient of passive earth pressure, which depends on the angle of internal friction of the soil and the angle of inclination of the wall face (dimensionless). It is defined as:

K_p = \tan^2 \left( 45° + \frac{\phi'}{2} \right)

Bearing capacity assessment

See shallow foundation theory.

Overturning assessment

The safety factor against rotation is calculated using moments about the toe of the wall:

FS = \frac{\sum M_R}{\sum M_O}

Where:

$FS$ : Safety factor.
$\sum M_R$ : resisting moments, associated with the self-weight and passive earth pressure of the structure ( $\text{kN m}$ ).
$\sum M_O$ : overturning moments, associated with active earth pressure and hydrostatic pressure ( $\text{kN m}$ ).

Sliding assessment

The safety factor against sliding is calculated using the horizontal forces acting on the wall:

FS = \frac{\sum F_R}{\sum F_S} = \frac{\left( \sum V \right) \tan \delta + B c_a' + P_p}{P_H}

Where:

$FS$ : Safety factor ( $\text{kN}$ ).
$F_R$ : Resisting forces, including friction and adhesion at the base, as well as passive soil thrust ( $\text{kN}$ ).
$\delta$ : Angle of friction between the structure and the foundation soil. $\delta = \frac{2}{3} \phi'$ ( $°$ ).
$c_a$ : Adhesion between the structure and the foundation soil. $c_a = \frac{2}{3} c'$ ( $\text{kN/m}^2$ ).

References

Das, B. M., & Sivakugan, N. (2018). Principles of Foundation Engineering.