🏗️ Construction — deep excavation monitoring Live model
You are the site engineer for a 15 m excavation braced by five levels of struts, with a building 6 m behind the wall. Every simulated day the model digs at your rate, lets the strut crew install the next level, bends the wall according to how much of it is unsupported, spreads the movement into a settlement trough under the building, and lowers the groundwater wherever you pump. You see what the site sees: inclinometer and settlement readings with measurement error. Educational simulation only — the numbers are illustrative and this is not engineering design advice.
What you will learn
Why the unsupported height decides wall movement: stiffness falls with the fourth power of the span, so one over-dug metre costs far more than one metre dug on time.
How dewatering keeps the excavation base from lifting — and why the same drawdown consolidates the clay under a neighbouring building.
The observational method in practice: trigger levels, noisy readings, and contingency actions planned before they are needed.
Simulator
Time 0 d
━Strut installed
┅Strut being installed
▼Over-excavated face
✓Below alert level
!Alert level reached
‼Action level reached
▤Soil berm
┄Aquifer pressure head
Controls
Metres of depth removed per day. 0 stops the excavators.
Stop the dig 0.5 m below the next strut level until that strut is installed.
Jacking force locked into each new strut, as a share of its design load. Applies to struts installed from now on.
Leave or place soil against the foot of the wall: it props the open face (−2 m unsupported height) but no digging is possible while it is there.
Pumping from the wells inside the pit. Lowers the aquifer pressure under the base — and around it.
Water injected near the building to hold the groundwater up under it. It is the pumped water re-used, and injection wells clog, so at most 55 % of the pumped flow can go back in. It also pushes back on the dewatering.
Indicators
Building settlement (reading)
0.0mm
normal
Wall deflection (inclinometer)
0.0mm
normal
Building angular distortion
0.00‰
normal
Base uplift safety factor
1.97
normal
Building settlement (model)
0.0 mm
Wall deflection (model)
0.0 mm
Settlement change per day
0.0 mm/d
Excavation depth
0.0 m
Unsupported height
0.0 m
Lowest strut load
0 %
Strut levels installed
0
Drawdown under the pit
0.0 m
Drawdown under the building
0.0 m
Consolidation settlement
0.0 mm
Days over-excavated
0 d
Water pumped so far
0 10³ m³
Recharge actually injected
0 m³/h
Trend
Crisis scenarios
Level 1 · Dig at the pace of the struts
The excavators can take 0.8 m a day and the programme wants that pace. The strut crew needs two days per level and can only start once the dig is 0.5 m below it, so at full pace the face runs ahead of the support. The owner of the building behind the wall has agreed a 12 mm settlement limit. Reach the 15 m formation within the 40 days, keep the building under 12 mm and the wall deflection under 15 mm.
Building settlement never above 12 mm
Wall deflection at the end ≤ 15 mm
Reach 15 m depth
Level 2 · Dewatering under a neighbour
A confined sand aquifer lies 22 m down. Below about 9 m the soil left under the base can no longer hold its water pressure down, so the aquifer must be pumped as the dig goes deeper — base uplift safety factor at least 1.2 throughout. On day 8 the dewatering crew opens the wells to 450 m³/h. A clay layer sits on top of the aquifer under the building next door. The discharge permit allows 280 thousand m³ for the whole job. Reach 15 m in 45 days with the building's settlement at the end within 30 mm.
Base uplift safety factor never below 1.2
Building settlement at the end ≤ 25 mm
Total pumped ≤ 280 thousand m³ (discharge permit)
Reach 15 m depth
Level 3 · The steel is late
The contractor digs continuously at 0.7 m a day with no hold points, and the strut crew has kept up so far. On day 15, with the face already at the fourth strut level, the steel for that level is held up for a week. Struts 1–3 are in. Keep the lowest strut within its design load and the wall deflection under 30 mm, and still reach 15 m by day 30.
Lowest strut load never above 100 % of design
Wall deflection at the end ≤ 30 mm
Reach 15 m depth
Basis — the model behind the numbers
Every relation the simulator uses, with its source. Constants marked as assumptions are illustrative calibrations.
Clough & O'Rourke system stiffness: the wall's bending stiffness over the fourth power of the unsupported span.
S = EI / (γw · h⁴), h = depth − lowest strut level (unsupported height)[3][5]
Each metre dug adds deflection at a rate that rises as system stiffness falls; preload cuts it, an open face deeper than the hold point creeps.
Δδh = ΔH · ρ(S) · (1 − 0.8·preload); ρ(%) = clip(2.3 − 0.7·log10 S, 0.12, 1.6); creep 2.5 mm/d per m of h above 3.5 m (berm −2 m)[3][5][10]Illustrative magnitudes for teaching, not values for any real site.
Ground settlement behind the wall: about 0.75 × the wall deflection, flat to 0.75 H, fading to zero at 2 H (soft-to-medium clay envelope).
δv,max = 0.75·δh,max; δv(d) = δv,max for d ≤ 0.75H, × (2 − d/H)/1.25 to 0 at d = 2H[3][4]
The soil left below the base must outweigh the confined water pressure pushing up from the aquifer.
Thiem steady flow: drawdown falls with the logarithm of distance from the wells; recharge wells add the opposite effect.
s(r) = Q/(2πT)·ln(R/r) − Q_r/(2πT)·ln(R/r_r) (steady radial flow, superposition; heads lag the steady state with τ = 1.5 d); Q_r ≤ 0.55·Q[9]Illustrative magnitudes for teaching, not values for any real site.
Terzaghi 1-D consolidation: lowered water pressure diffuses into the clay over days, and the clay compresses as effective stress rises.
Angular distortion: difference in settlement across the building divided by its length, against Bjerrum's limits.
β = (s_near − s_far) / L; 1/500 = 2 ‰ (limit where cracking is not acceptable), 1/300 = 3.3 ‰ (first cracking)[6][7]
Peck apparent earth pressure on the lowest strut over its tributary height; the deeper the open face, the more it carries.
P = 0.3·γ·H · (half span above + h) · 5 m ≥ preload; shown as % of design load 2400 kN[2]Illustrative magnitudes for teaching, not values for any real site.
Instrument readings carry measurement error — read trends, not single values.
reading = true value + N(0, σ); σ = 0.5 mm (settlement points), 1.0 mm (inclinometer)[1]Illustrative magnitudes for teaching, not values for any real site.
Constants used by the model
final depth 15 m · struts at 1, 4, 7, 10, 13 m, 5 m apart along the wall, crew starts 0.5 m below a level and needs 2 days · over-excavation allowance 4 m unsupported · wall 0.8 m concrete (EI = 1.28 GN·m²/m per m) · γ = 19 kN/m³ · building 12 m long, near edge 6 m behind the wall · water table 1 m · aquifer T = 300 m²/d, R = 400 m, excavation radius 12 m, recharge line 4 m behind the wall (effective radius 3 m) · clay 5 m above the aquifer, m_v = 0.2 /MPa, c_v = 0.15 m²/d · ground factors lognormal (σ 0.10 wall, 0.15 m_v, 0.20 c_v) · base unworkable below FS 1.05 · recharge capped at 55 % of the water pumped (supply from the discharge, well clogging)Illustrative magnitudes for teaching, not values for any real site.
Randomness: a seeded mulberry32 generator; distributions used — uniform, exponential (inverse CDF), normal (Box–Muller), Poisson (Knuth). The seed is shown and shareable.
R. B. Peck — Deep excavations and tunneling in soft ground (apparent earth-pressure diagrams for braced cuts) — Proc. 7th ICSMFE, Mexico City, State-of-the-Art Volume, 225–290, 1969
G. W. Clough, T. D. O'Rourke — Construction induced movements of in-situ walls (system stiffness EI/(γw·h⁴), settlement envelopes) — ASCE Geotechnical Special Publication 25, Design and Performance of Earth Retaining Structures, 439–470, 1990
C.-Y. Ou — Deep Excavation: Theory and Practice (upheaval / uplift check against a confined aquifer, dewatering, strut preload) — Taylor & Francis, 2006