Eurocode 7 Bearing Resistance Calculator

Check spread foundation bearing resistance according to Eurocode 7 (EN 1997-1) using a Terzaghi-type expression with partial factors, shape and inclination factors, and eccentric loading.

Bearing Resistance Calculator (EN 1997-1 Annex D style)

This tool is intended for preliminary design and educational use. Always verify results against the relevant National Annex and project specifications.

1. Foundation geometry

2. Soil parameters (effective values)

3. Design loads at foundation level (ULS)

Moments are taken at the foundation base. Positive values increase eccentricity in the corresponding direction.

4. Partial factors & options

Eurocode 7 bearing resistance – theory and formulas

Eurocode 7 (EN 1997-1) defines the bearing resistance of a foundation as the ultimate resistance of the ground to vertical loading. For spread foundations, Annex D provides a Terzaghi-type bearing capacity expression that can be used in conjunction with the partial factor design format.

Ultimate bearing capacity expression

For a rectangular footing of width \(B\) and length \(L\) at depth \(D_f\), on homogeneous soil with effective cohesion \(c'\), friction angle \(\varphi'\), and effective unit weight \(\gamma'\), a commonly used expression is:

\[ R_k = c' \, N_c \, s_c \, i_c \, B' L' \;+\; q' \, N_q \, s_q \, i_q \, B' L' \;+\; 0.5 \, \gamma' \, B' \, N_\gamma \, s_\gamma \, i_\gamma \, B' L' \] where:
  • \(R_k\) = characteristic bearing resistance (kN)
  • \(B', L'\) = effective foundation dimensions accounting for eccentricity (m)
  • \(q' = \gamma' D_f + q_0\) = effective overburden at foundation level (kPa)
  • \(N_c, N_q, N_\gamma\) = bearing capacity factors
  • \(s_c, s_q, s_\gamma\) = shape factors
  • \(i_c, i_q, i_\gamma\) = inclination factors

Bearing capacity factors for drained conditions

For effective stress design in drained conditions, the bearing capacity factors can be expressed in terms of \(\varphi'\) (in radians):

\[ N_q = e^{\pi \tan\varphi'} \tan^2\left(45^\circ + \frac{\varphi'}{2}\right) \] \[ N_c = \frac{N_q - 1}{\tan\varphi'} \quad (\varphi' > 0) \] \[ N_\gamma = 2 (N_q + 1) \tan\varphi' \]

For purely cohesive soil (\(\varphi' = 0\)), Eurocode 7 recommends using appropriate values from the National Annex or literature; this calculator uses a simplified approach and warns when \(\varphi' \approx 0\).

Shape and inclination factors (simplified)

Several slightly different sets of shape and inclination factors exist in the literature and National Annexes. This calculator uses a commonly adopted set for rectangular footings:

Shape factors (for \(L \ge B\))

\[ s_q = 1 + \frac{B'}{L'} \] \[ s_c = 1 + N_q \frac{B'}{L'} \] \[ s_\gamma = 1 - 0.4 \frac{B'}{L'} \]

Inclination factors (for vertical load \(V_d\) and horizontal load \(H_d\))

\[ i_q = \left(1 - \frac{H_d}{V_d}\right)^2 \quad (H_d \le 0.5 V_d) \] \[ i_c = i_q - \frac{1 - i_q}{N_c} \] \[ i_\gamma = i_q^2 \]

If you choose to disable these factors in the calculator, all \(s\) and \(i\) values are set to 1.0, which is conservative for some cases and unconservative for others. Always check against your National Annex.

Effective foundation dimensions for eccentric loading

Eccentric vertical loading reduces the effective area of the footing. For design, a common approximation is:

\[ e_x = \frac{M_y}{V_d}, \quad e_y = \frac{M_x}{V_d} \] \[ B' = B - 2 e_x, \quad L' = L - 2 e_y \]

If \(B' \le 0\) or \(L' \le 0\), the footing is too small for the given eccentricity and the calculator will flag an error.

From characteristic to design bearing resistance

Eurocode 7 allows different design approaches (DA1, DA2, DA3). In this calculator we use a simple resistance-factor format:

\[ R_d = \frac{R_k}{\gamma_R} \]

where \(\gamma_R\) is a global resistance factor chosen by the user (for example 1.4 or 1.6 for spread foundations, depending on the National Annex and design approach).

Worked example (illustrative)

Consider a rectangular footing \(B = 2.0\) m, \(L = 3.0\) m at depth \(D_f = 1.0\) m on dense sand with \(\gamma' = 18\) kN/m³, \(c' = 0\), \(\varphi' = 35^\circ\). The design vertical load is \(V_d = 1500\) kN, horizontal load \(H_d = 50\) kN, and no moments. Assume \(\gamma_R = 1.4\).

  1. Compute \(q' = \gamma' D_f = 18 \times 1.0 = 18\) kPa.
  2. Compute bearing capacity factors for \(\varphi' = 35^\circ\): \(N_q \approx 41.4\), \(N_c \approx 73.3\), \(N_\gamma \approx 68.4\).
  3. With no eccentricity, \(B' = B = 2.0\) m, \(L' = 3.0\) m.
  4. Shape factors: \(s_q = 1 + B'/L' = 1 + 2/3 \approx 1.67\), \(s_\gamma = 1 - 0.4 B'/L' \approx 0.73\). Since \(c' = 0\), the cohesion term is zero.
  5. Inclination factors: \(i_q = (1 - H_d/V_d)^2 = (1 - 50/1500)^2 \approx 0.94\), \(i_\gamma = i_q^2 \approx 0.88\).
  6. Characteristic resistance (friction term only): \[ R_k \approx q' N_q s_q i_q B' L' + 0.5 \gamma' B' N_\gamma s_\gamma i_\gamma B' L' \]
  7. Divide by \(\gamma_R\) to obtain \(R_d\) and compare with \(V_d\). The calculator performs all these steps automatically.

Limitations and good practice

  • This tool is aimed at shallow spread foundations on homogeneous soil or rock.
  • For layered profiles, soft strata, or complex failure mechanisms, consider numerical analysis or more advanced Annex F methods.
  • Always use soil parameters derived from appropriate site investigation and laboratory/field testing.
  • Check settlement and serviceability separately; this calculator only addresses ultimate bearing resistance.

Frequently asked questions

Can I use undrained parameters (cu, φ = 0)?

In undrained conditions, Eurocode 7 often uses total stress design with undrained shear strength \(c_u\) and \(\varphi = 0\). The bearing capacity expression simplifies and the factors differ from the drained case. This calculator is primarily configured for drained effective stress design; if you use \(c' = c_u\) and \(\varphi' = 0\), treat the results with caution and cross-check with your National Annex.

How do I choose γR?

The resistance factor \(\gamma_R\) depends on the design approach (DA1, DA2, DA3) and the National Annex. Some Annexes provide separate factors for base resistance and side resistance, or for different limit states. For preliminary checks, values between 1.3 and 1.6 are common for spread foundations, but you must confirm the correct value for your jurisdiction.

What if the utilization ratio is greater than 1.0?

A utilization \(\eta = E_d / R_d > 1.0\) means the design load exceeds the design bearing resistance. You may need to increase the footing size, reduce the load, improve the ground (e.g., compaction, replacement, reinforcement), or adopt a different foundation type.