Method and assumptions

Every footing page relies on these units, conventions and assumptions; the method then runs in the order below, with a page for each part.

Units and conventions

• SI units: m, kN, kPa, kN/m³ and degrees. A strip footing is analysed per metre of length, in kN/m and kN·m/m.
• Depths are measured down from the ground surface: the strata (top down), the water table (negative when water stands above the ground) and the embedment depth $D_f$ of the base.
• $B$ is the width and $L$ the length. The horizontal load $H$ acts along $B$. In the method $B$ is the shorter side, as in Das & Sivakugan: a footing entered wider than long gives the same result as with its sides swapped. The moment $M_B$ moves the load off centre across the width and $M_L$ along the length; the checks use a moment’s magnitude, and its sign only says which edge carries more.
• The unit weight of water is $\gamma_w = 9.81$ kN/m³.
• The studio’s form writes $c'$, $\varphi'$, $E$ and $\nu$; the equations write $c$, $\phi$, $E_s$ and $\mu_s$.
• $H$ is the horizontal load in the bearing capacity and the depth of influence in the settlement. $B'$ is the effective width in the bearing capacity and, as in the textbook, $B/2$ in the settlement.

Assumptions

• $V$ is the load that reaches the soil at the base: Rischio adds no weight of the footing or of the soil over it.
• The moments act at the base. $H$ enters only through the inclination of the load; a moment it makes about the base belongs in $M_B$.
• $c$ and $\phi$ are those of the stratum the base rests on (at a boundary, the lower one). The strata above only add overburden; deeper strata enter $\gamma'$ and the settlement, but their strength never enters $q_u$.
• The ground surface is level.
• The settlement is computed when every stratum has $E_s$ and $\mu_s$.

Method

The calculation runs in the order of the calculation report. The moments move the resultant off centre, and its eccentricities give the effective area; the horizontal load gives the inclination of the load. The general bearing capacity equation gives $q_u$, the linear contact pressure gives $q_{max}$ and $q_{min}$, and the factor of safety compares $q_u$ with $q_{max}$; the eccentricity checks come next. Bearing capacity covers all of this, every factor included. Last comes the elastic settlement at the centre of the base: Settlement. Equations lists every step with its equation.

References

• Das, B. M., & Sivakugan, N. (2017). Principles of Foundation Engineering, SI edition, 9th ed. Cengage Learning. It gives every factor in these pages with its original source: Prandtl, Reissner, Vesic, De Beer, Hansen, Meyerhof, Hanna and Meyerhof, Steinbrenner and Fox.