Shallow bearing capacity standard

Equations

$$q_{ult} = c' N_c + q N_q + 0.5 \gamma B N_{\gamma}$$ $$q = \gamma D_f$$ $$q_{allow,net} = \frac{q_{ult} - q}{FS}$$

State any shape, depth, inclination, groundwater, or eccentricity modifiers explicitly instead of assuming them from context.

Variables and Units

• $c'$ = effective cohesion in consistent stress units.
• $\gamma$ = unit weight in consistent force-per-volume units.
• $B$ = footing width and $D_f$ = embedment depth in consistent length units.
• $N_c$, $N_q$, and $N_{\gamma}$ = bearing-capacity factors tied to the friction angle and selected formulation.
• $FS$ = stated factor of safety used to move from ultimate to net allowable bearing pressure.

Required Assumptions

• Drained loading conditions apply at the footing level.
• Footing geometry and surcharge are known well enough for the selected bearing-capacity relationship.
• Layering or groundwater changes near the footing base are screened before use.

Validity Ranges

• Intended for shallow foundations where the drained bearing-capacity formulation is appropriate.
• Use additional review when strong layering, nearby slopes, or groundwater changes materially alter the stress path.

Implementation Checks

• Confirm drained conditions, groundwater position, footing geometry, and surcharge assumptions before using the closed-form method.
• Check whether settlement, punching, nearby slopes, or excavation staging govern before finalizing the allowable pressure.
• Record whether the formulation follows Terzaghi, Meyerhof, or another explicitly cited local adaptation.

Known Limitations

• The method is a screening standard, not a substitute for full settlement or serviceability checks.
• Local construction sequencing and excavation effects can invalidate the drained assumption.

References

• Terzaghi, K. (1943). Theoretical Soil Mechanics.
• Meyerhof, G. G. (1963). Some recent research on the bearing capacity of foundations.

Evidence to Attach

• Borehole, CPT, or laboratory parameters used to derive c-prime, friction angle, and unit weight.
• Groundwater observations, footing geometry sketch, and load combination summary.
• Settlement check or other serviceability review showing why bearing capacity is not the only governing criterion.

Worked Example

Confirm drained conditions, footing width, embedment, and surcharge before applying the bearing-capacity relationship, then compare the result with settlement and constructability checks.