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EC7 Bearing Capacity of a Single Shallow Footing — Drained & Undrained (SLS & ULS DA1‑C1/C2)
Disclaimer. This tool follows EC7 conventions. Results are for preliminary use only and must be checked and approved by a suitably qualified engineer before reliance. PHICON accepts no liability without formal verification/approval.
1. Project Details
| Field | Value |
|---|---|
| Project | |
| Location | |
| Calculation | |
| Designer | |
| Checker | |
| Date | |
| Revision | |
| Notes |
2. Standards & Design Approach
- EN 1997‑1 (Eurocode 7), §6.5.2 and Annex F.
- Design Approach 1 combinations **C1** and **C2** are evaluated for ULS; SLS uses characteristic values.
3. Geometry & Soil Inputs (Characteristic — Live Editable)
| Parameter | Symbol | Value | Unit |
|---|---|---|---|
| Footing Width | B | m | |
| Footing Length | L | m | |
| Embedment Depth | Df | m | |
| Depth to water table | zw | m | |
| Foundation thickness | tf | m | |
| Unit Weight | γk | kN/m³ | |
| Effective Cohesion | c′k | kPa | |
| Friction Angle | φ′k | ° | |
| Undrained Shear Strength | cu,k | kPa | |
| Interface friction (base) | δk | ° | |
| Base adhesion | ca,k | kPa | |
| Derived values (water table) | |||
| Submerged unit weight | γ′ | – | kN/m³ |
| Effective overburden at base | q′ | – | kPa |
| Effective unit weight at base | γbase | – | kN/m³ |
| Characteristic Actions | Symbol | Value | Unit |
|---|---|---|---|
| Vertical | Vk | kN | |
| Horizontal (B‑dir) | HB,k | kN | |
| Horizontal (L‑dir) | HL,k | kN | |
| Moment (about B) | MB,k | kNm | |
| Moment (about L) | ML,k | kNm | |
| Foundation mass effects (tf at γconc=25 kN/m³, soil γk) | |||
| Self-weight of foundation | Gconc,k | – | kN |
| Soil removed within footprint | Wsoil,k | – | kN |
| Net added permanent action | ΔGk | – | kN |
| Vertical incl. ΔG | Vk,tot | – | kN |
| ULS design actions below are auto-calculated from characteristic values and partial factors. | |||
4. Characteristic & ULS Design Actions
| Action | Symbol | DA1‑C1 | DA1‑C2 | Unit |
|---|---|---|---|---|
| Vertical | VEd | – | – | kN |
| Horizontal (B) | HB,Ed | – | – | kN |
| Horizontal (L) | HL,Ed | – | – | kN |
| Moment (about B) | MB,Ed | – | – | kNm |
| Moment (about L) | ML,Ed | – | – | kNm |
5. Factors
Partial Factors (editable)
| γc′ | |
| γφ′ | |
| γcu | |
| γγ | |
| γG (perm. V) | |
| γQ (var. H,M) |
Resistance Factors — vertical bearing & sliding
| γR;v (DA1‑C1) | |
| γR;v (DA1‑C2) | |
| γR;h (DA1‑C1) | |
| γR;h (DA1‑C2) |
Inclination Factors (SLS representative)
| ic | – |
| iq | – |
| iγ | – |
Bearing Capacity Factors (from φ′k)
| Nc | – |
| Nq | – |
| Nγ | – |
Shape Factors (auto)
| sc | – |
| sq | – |
| sγ | – |
Combination Factors Summary — DA1‑C1 vs DA1‑C2 (editable)
Use these to override per‑combination factors (actions/materials). Presets from the National Annex dropdown can be adjusted here.
| Type | Symbol | DA1‑C1 | DA1‑C2 | Applied to |
|---|---|---|---|---|
| Actions (vertical) | γG | V | ||
| Actions (horizontal/moment) | γQ | H, M | ||
| Materials — cohesion | γc′ | c′ | ||
| Materials — friction | γφ′ | φ′ | ||
| Materials — unit weight | γγ | γ | ||
| Materials — undrained strength | γcu | cu |
6. Results
SLS (Characteristic)
| Case | qd,SLS |
|---|---|
| Drained | – |
| Undrained | – |
ULS (qRd)
| Case | qRd |
|---|---|
| Drained — DA1‑C1 | – |
| Drained — DA1‑C2 | – |
| Undrained — DA1‑C1 | – |
| Undrained — DA1‑C2 | – |
ULS Sliding Resistance (qRd;h)
| Case | HEd | VEd | RRd;h = (V′·tanδd + ca,d·A′)/γR;h | Unit |
|---|---|---|---|---|
| DA1‑C1 | – | – | – | kN |
| DA1‑C2 | – | – | – | kN |
δd from δk via γφ′ of the combination; A′ uses B′×L′ per combination.
ULS Overturning (middle‑third check)
| Item | Symbol | Value | Unit |
|---|---|---|---|
| Limit eccentricity (B‑dir) | B/6 | – | m |
| Limit eccentricity (L‑dir) | L/6 | – | m |
| Eccentricity C1 (B‑dir) | eB,C1=MB,Ed/VEd | – | m |
| Eccentricity C1 (L‑dir) | eL,C1=ML,Ed/VEd | – | m |
| Eccentricity C2 (B‑dir) | eB,C2=MB,Ed/VEd | – | m |
| Eccentricity C2 (L‑dir) | eL,C2=ML,Ed/VEd | – | m |
| Utilisation C1 (B‑dir) | ηOT,B,C1=eB,C1/(B/6) | – | – |
| Utilisation C1 (L‑dir) | ηOT,L,C1=eL,C1/(L/6) | – | – |
| Utilisation C2 (B‑dir) | ηOT,B,C2=eB,C2/(B/6) | – | – |
| Utilisation C2 (L‑dir) | ηOT,L,C2=eL,C2/(L/6) | – | – |
7. Conclusions — Utilisation
Utilisation is defined as η = V / (q × A′) for bearing, H / R for sliding, and e / (limit) for overturning.
| Case | V | q or R | A′ | η (ratio) | η (%) | Status |
|---|---|---|---|---|---|---|
| SLS (Characteristic, Drained) | – | – | – | – | – | – |
| SLS (Characteristic, Undrained) | – | – | – | – | – | – |
| ULS — DA1‑C1 (Drained) | – | – | – | – | – | – |
| ULS — DA1‑C1 (Undrained) | – | – | – | – | – | – |
| ULS — DA1‑C2 (Drained) | – | – | – | – | – | – |
| ULS — DA1‑C2 (Undrained) | – | – | – | – | – | – |
| ULS — Sliding (DA1‑C1) | – | – | – | – | – | – |
| ULS — Sliding (DA1‑C2) | – | – | – | – | – | – |
8. Governing Formulas
SLS — Drained bearing pressure
\[ q_{d,SLS}^{(D)} = c’_k N_c s_c i_c \; + \; \gamma_k D_f N_q s_q i_q \; + \; 0.5\,\gamma_k B’ N_{\gamma} s_{\gamma} i_{\gamma} \]
—
SLS — Undrained bearing pressure
\[ q_{d,SLS}^{(U)} = c_{u,k} N_c \quad (N_c = 5.14) \]
—
ULS — Drained, DA1‑C1 (with resistance factor)
\[ q_{Rd}^{(D,C1)} = \frac{\;c’_d N_c s_c\; + \; \gamma_d D_f N_q s_q i_q \; + \; 0.5\,\gamma_d B’ N_{\gamma} s_{\gamma} i_{\gamma}\;}{\gamma_{R;v}} \]
—
ULS — Drained, DA1‑C2 (with resistance factor)
\[ q_{Rd}^{(D,C2)} = \frac{\;c’_d N_c s_c\; + \; \gamma_d D_f N_q s_q i_q \; + \; 0.5\,\gamma_d B’ N_{\gamma} s_{\gamma} i_{\gamma}\;}{\gamma_{R;v}} \]
—
ULS — Undrained, DA1‑C1
\[ q_{Rd}^{(U,C1)} = \frac{c_{u,k}}{\gamma_{cu,C1}} N_c \; / \; \gamma_{R;v} \]
—
ULS — Undrained, DA1‑C2
\[ q_{Rd}^{(U,C2)} = \frac{c_{u,k}}{\gamma_{cu,C2}} N_c \; / \; \gamma_{R;v} \]
—
ULS — Sliding resistance
\[ R_{Rd;h} = \frac{ V_{Ed} \tan\delta_d + c_{a,d} A’ }{\gamma_{R;h}} \]
—
—
ULS — Overturning (kern / middle‑third)
\[ e_B = \frac{M_{B,Ed}}{V_{Ed}},\quad e_L = \frac{M_{L,Ed}}{V_{Ed}},\quad e_B \le \frac{B}{6},\; e_L \le \frac{L}{6} \]
—
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