Braced excavation
A flexible excavation wall (sheeting, or soldier piles and lagging) supported by struts or rakers inside the cut, or by ground anchors: the apparent earth pressure diagrams of UFS 3-220-20 (DM7.2, 2026) 4-8.3, the support loads by the tributary area or the hinge method, the wall and wale moments, and the stability of the base against heave (DM7.2 2-4.3.3).
Inputs of the braced excavation #
- Excavation: soil (sand, or undrained clay whose envelope follows the stability number N0 = γH/su: stiff clay when N0 ≤ 4, soft to medium clay above), support (internal bracing, or ground anchors with the FHWA 1999 diagrams; DM7.2 leaves the use of the FHWA diagrams for preloaded struts to the engineer), depth H, width B (and length L for Bjerrum and Eide), the support levels, their horizontal spacing, and the method for the support loads.
- Soil and water: γ, φ' (sand) or su above and below the base (clay); for sand below the base γ2 and φ'2 (Figure 2-7(a)); the depth to a firm layer below the base (B1 = 0.7B for deep clay); whether deep soft normally consolidated clay underlies the cut (m = 0.4·FBH in Figure 4-52); the stiff clay coefficient (0.4, or 0.2 for small movements and a short construction period); a uniform surcharge with its pressure coefficient (Ka for sand; the engineer's choice for clay); and the water table behind the wall with the cut dewatered to the base.
- Base stability: the method for clay (DM7.2 Figure 2-7(b) flexible wall, 2-7(c) very stiff wall with adhesion α, Terzaghi 1943, or Bjerrum and Eide 1956), the wall embedment below the base, and the required factor of safety (1.5, DM7.2 2-4.3.3).
- Wall and wale: arching in the lower spans (DM7.2 4-8.3.1: pressures may be reduced to 80 % in all but the upper span), and the section modulus and Fy of the wall per foot and of the wale (0 reports the moment only).
Auto-design varies the horizontal spacing of the struts or anchors (1-ft steps) for the entered wale. See Auto-design.
Checks performed #
| Check | Basis |
|---|---|
| Apparent pressure, sand | Internal: uniform 0.65·Ka·γ·H; anchors: trapezoid σH = 0.65·Ka·γ·H²/(H − H1/3 − Hn+1/3) (Figure 4-51) |
| Apparent pressure, soft to medium clay | Internal: Ka = 1 − m·4su/γH, σH = Ka·γ·H reached at 0.25H; anchors: Ka = 0.22 (4 < N0 ≤ 5.14) or 1 − 4su/γH + 2√2(d/H)(1 − 5.14su,b/γH) (Figure 4-52) |
| Apparent pressure, stiff clay | 0.2 to 0.4·γ·H over the middle (internal) or between the anchor ramps (Figure 4-53) |
| Support loads | Tributary area (half the distance to the next support) or hinge method (simple spans, the top cantilever to the first level, the lowest span to the base) |
| Wall moment | The top cantilever exactly; spans w·l²/10 with the largest pressure on the span; first yield Fy·S with 1.6 H (LRFD) |
| Wale moment | T·s²/10 for a continuous wale; first yield |
| Base stability, sand | FBH = 2·Nγ·(γ2/γ1)·Ka·tanφ'1 (Figure 2-7(a), Vesić Nγ) |
| Base stability, clay | (5.7·su,b·B1 + su,h·H [+ (1 + α)·su,d·D]) / (γ·H·B1 + q·Bs) (Figure 2-7(b), (c)); Terzaghi 5.7·su·B1/(γHB1 + qB1 − su·H); Bjerrum-Eide Nc·su/(γH + q) |
| Force on buried sheeting | When FBH is below the required value: P'H of Figure 2-7(b) |
The drawings show a section through one side of the cut (wall, retained ground, base, supports with their loads per foot, water table) and the pressure diagram used.
Limitations #
- Ground movements and their effect on neighbours (DM7.2 2-4.4, Table 2-8), seepage and piping, point and line surcharges (DM7.2 Figure 4-18), and the strut, anchor and connection design are the engineer's.
- One soil above the base: layered retained soil should be averaged by the engineer, as the apparent diagrams assume.
- Terzaghi (1943) and Bjerrum and Eide (1956) are written from knowledge (to confirm against the original papers); the Skempton Nc expression used for Bjerrum-Eide caps H/B at 2.5.
- The apparent diagrams suit deep (over about 20 ft) and relatively wide cuts (DM7.2 4-8.3).
Verification examples #
Verification status: 9 values compared in 2 examples (1 published, 1 hand calculations from the cited equations): 9 within tolerance, 0 recorded deviations. Thin: only 1 published example. Code basis: the provisions it uses were read in the target edition.
Published worked example and hand calculations (backend/tests/test_verify_braced_excavation.py):
| Source | What it checks | Published | ILX Calcs |
|---|---|---|---|
| UFS 3-220-20 Figure 4-55: 12 ft wide, 20 ft deep cut in soft clay, su = 400 psf | FBH, Ka, σh | 1.35, 0.64, 1.54 ksf | (test run) |
| same | Resultant and its height, force on the buried sheeting | 27 kips/ft, 8.8 ft, 1.6 kips/ft | (test run) |
| Hand, Figure 4-51: sand φ' = 30°, H = 24 ft, levels 4, 12, 20 ft | σH, tributary loads | 624 psf, 4.99 kips/ft | (test run) |
The example's 10-kip point surcharge is not modelled; its wall pressure from that load (Figure 4-18) is not compared.