Theory

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

The content is aimed at providing a clear understanding of how calculations are performed within the software, facilitating both the interpretation of 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 the soil ( $\text{kN/m}^3$ ).
$H$ : Height of the wall ( $\text{m}$ ).
$K_a$ : Active earth pressure coefficient, which depends on the soil internal friction angle and the inclination angle 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 the soil ( $\text{kN/m}^3$ ).
$D_f$ : Embedment depth ( $\text{m}$ ).
$K_p$ : Passive earth pressure coefficient, which depends on the soil internal friction angle and the inclination angle of the wall face (dimensionless). It is defined as:

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

Bearing Capacity Evaluation

See shallow foundation theory.

Overturning Evaluation

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

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

Where:

$FS$ : Factor of safety.
$\sum M_R$ : Resisting moments, associated with the structure’s self-weight and passive earth pressure ( $\text{kN m}$ ).
$\sum M_O$ : Overturning moments, associated with active earth pressure and hydrostatic pressure ( $\text{kN m}$ ).

Sliding Evaluation

The factor of safety 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:

$FS$ : Factor of safety ( $\text{kN}$ ).
$F_R$ : Resisting forces, including friction and adhesion at the base as well as passive earth pressure ( $\text{kN}$ ).
$\delta$ : Friction angle 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.